This book describes an Action Research project within the researcher's practice as a teacher educator in Rwanda. A teaching style informed by the Theory of Didactical Situations in Mathematics (Artigue, 1994, Brousseau, 1997, 2004, Douady, 1991) and by the Zone of Proximal Development (Gallimore & Tharp, 1990, Meira & Lerman, 2001, Vygotsky, 1978) was conducted with first-year mathematics student teachers in Rwanda. The aim of the teaching model was to develop the student teachers' understanding of the concepts of the definite and the indefinite integrals and their link through the fundamental theorem of calculus. The findings of the analysis answer the research questions, on the one hand, of what concept images (Tall & Vinner, 1981, Vinner & Dreyfus, 1989) of the underlying concepts of integrals student teachers exhibit, and how the student teachers' concept images evolved during the teaching.