In recent years, there have been several studies in mathematics education basing on the variation theory and the model of Learning Study that involves co-operation between teachers and researchers in an iterative process. Most of these studies have focused on the teaching and learning of elementary school mathematics rather than topics in advanced mathematics. In this paper, we discuss some challenges and possibilities of the Learning Study model and the variation theory when developing the teaching of mathematics at advanced levels. More precisely, we report on a series of teaching experiments on the definite integral concept. The experiments were carried out at a Swedish university. The data of this study consists of the documents on the observation of three lectures and the students’ answers to pre and post tests. Both engineering and teacher students participated. In the analysis of the data, we applied statistical methods. Although the series consisted only of three lectures, it revealed that the students’ understanding about certain – but not necessarily all – aspects of the definite integral concept can be enhanced by using the Learning Study model.