© 2014 American Association of Physics Teachers. We report on semi-quantitative research into students' difficulties with integration in an intermediate-level electromagnetism course with cohorts of about 50 students. We have found that before they enter the course, students view integration primarily as a process of evaluation, even though viewing integration as a summation process would be more fruitful. We confirm and quantify earlier results that recognizing dependency on a variable is a strong cue that prompts students to integrate and that various technical difficulties with integration prevent almost all students from getting a completely correct answer to a typical electromagnetism problem involving integration. We describe a teaching sequence that we have found useful in helping students address the difficulties we identified.