This class note addresses the study of some fundamental concepts of the integral calculus of a real variable. It presents the basic ideas of the differential and the antiderivative of a function, the indefinite integral, differential equations with separable variables and examines the most relevant integration methods. It displays each of these topics in a precise and not too formal way. The work presents a right amount of solved examples that will serve as a model for the development of other proposed exercises (all with their answer). Besides, it offers a self-assessment section at the end of each chapter, which will help the student, on the one hand, to assess the progress made during the study and, on the other hand, to reinforce his journey into the world of integral calculus.