The file, from the culture and education committee, was drafted by Romanian deputy Damian Drăghici.
It was passed on Tuesday in a plenary vote by a margin of 482 votes to 146.
The document points out that the EU "should be more visible, and better integrated, in teaching materials and extracurricular activities."
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It stresses "the importance and the potential of a European approach to the teaching of history" and encourages the Commission to "continue its support for efforts to develop and promote an EU dimension in education as well as the mobility of educational actors."
Learning about the EU at school "should reflect both the role of member states in the development of the EU and the influence of the EU on national developments."
The report says member states should also "facilitate high-quality training on EU topics for teachers."
Responding to the adoption of the report, UKIP MEP Louise Bours, a member of the culture committee, said, "First the EU came for our money, then for the sovereignty of our courts and now they wish to fill our children's' heads with EU propaganda. What a crazy power trip these people are on.
"The EU should have no part in deciding or funding the text-books or inducing young teachers to give one-sided laudatory massages to the EU."
She added, "Education should be a solely national competence and under the discretion of parents, not MEPs in Brussels. The education of children should not be used and abused as a political tool to undermine 'Euroscepticism'. It is above that.
"A child's education should not be used as a political football.
"This vote today gives an idea of the direction of travel of the European institutions and its centralising thrust should worry both parents and democrats."
A Commission source said, "EU competence in education, youth and training policy is very limited. It is clarified in the EU treaty as being solely to support, coordinate or supplement the actions of the member states."
There are very few publications produced by EU institutions that are targeted towards schools. The Commission office says it has a policy of distributing publications only on demand and does not send out unsolicited copies.
A UK source said, "Schools are aware of their duties regarding impartiality and treatment of political issues and the Education Act 1996 requires maintained schools to prevent political indoctrination and secure the balanced treatment of political issues. This duty is reflected in the model funding agreement for academies and free schools.
"Pupils can be taught about Europe in the history and the citizenship national curricula. For example, at key stage three pupils should study British history from 1745 to 1901, including the development of empire, which can include a depth study, for example of India.
"Later, they should study the challenges for Britain, Europe and the wider world from 1901 to the present day, which can include the end of empire and Britain's place in the world since 1945. At key stage four, the citizenship education covers the UK's current relations with Europe, the Commonwealth, the United Nations and the wider world."
"While the UK government supports policy and best practice exchange on education among member states in the EU, the treaty is clear that education is a national competence. The EU has no power to intervene in the content of teaching or the organisation of national education systems.
"We do not agree that the EU should get more involved in the development of national curricula. The European Parliament report places no obligations on the UK or other member states.
"The EU should focus on contributing to the important area of international benchmarking on education standards through the publication of high quality comparative analysis and the promotion of policy and best practice exchange. And on helpful initiatives to promote links and exchanges between schools, particularly to support the learning of languages.
"UK legislation requires schools to deal with political issues, including consideration of the EU, in a balanced way. It is up to schools to decide how to achieve this.
"In citizenship education, pupils are taught about local, regional and international governance and the UK's relations with the rest of Europe, and the wider world. Pupils will be equipped with the skills to think critically and debate political questions.
"On citizenship, we have introduced various measures to promote the teaching of British values and the development of character in schools, much of which is in line with the content of the EU education ministers' declaration on countering extremism, in March 2015 in Paris."