The main task of the educational sphere is to create the necessary conditions for the student in the process of his formation, development as a person, taking into account the main values of humanity. Currently, various methods and methods of teaching are used in teaching mathematics. In this article, we focus on the use of problem methods in explaining the topic of the integral defined in mathematics lessons for students in general. The use of the problem method allows to increase the student's interest in independent search, deep thinking and solving any problems, ways out of a dead end. As everyone knows, there are various interesting problems on the topic of a certain integral (the main theorem is derived by the Newton-Leibniz formula). In particular, when calculating the area of figures on a plain, a curved trapezoid, to teach students effective ways to use a certain integral by setting a certain task. We applied this methodology to our topic and considered various tasks related to it.