This book is addressed to the students of Higher and Higher schools.

It contains four chapters.
In the 1st Chapter there is an understandable presentation of the theory of the Indefinite Integral and the methods for its calculation, accompanied by approximately 580 solved exercises. It was thought appropriate to include at the end of Chapter 1 a summary table of the methods of integration and a formula from Algebra, Trigonometry and Mathematical Analysis.
In the 2nd Chapter the theory of the definite integral is mentioned which is done in two ways. With regular typographic elements a simple presentation is made, while then with smaller elements a stricter presentation is made that concerns the students of the Mathematics departments. The same chapter contains a systematic grouping of exercises referring to the definite integral.
The 3rd Chapter contains the forms of Generalized Integrals with the relevant theory and solved exercises. The same chapter contains the smooth convergence (uniform convergence) of Generalized Integrals as well as the "Gamma" and "Beta" functions.
Finally, Chapter 4 contains applications of the definite integral (calculations of areas, volumes, etc.).