The training of mathematics teachers in universities in Colombia has as a transversal axis the resolution of problems based on their social and cognitive mission pillars. In this sense, this study relates to the re-signification and construction of the concept of definite integral (DI) (integral calculus) through socio-epistemological studies, action researches, and the typology of didactic situations. The results are obtained through content analysis, didactic sequences (GeoGebra), and a discussion group. The above allows us to conclude that the validation of meanings, historical contexts, and associated social practices leads to the construction of the concept of DI as a model of mathematical analysis. This structuring of knowledge from its epistemological framework enables the exploration of mathematical objects from the basic notions that emerge in the history of humanity and didactic processes that reconstruct the evolution of the concept in society.