This work suggests a methodology for the presentation of the topic "Solution of plane figures areas calculating problems " in the course "Integral calculus". The article is based on experience of mathematical analysis teaching in technical university and it will be useful both to teachers in conducting practical classes and to students in their independent work on the topic. The aim of this work is to help students to acquire and develop skills of integration methods application for various problems solving. When solving tasks on the areas calculation students have as a rule difficulties working with polar coordinates and functions defined parametrically. In this case, it is useful to consider the problem solution in different ways. The basic theoretical information is briefly stated in this article. The author gives examples and standard tasks that are necessary to improve integrating skills and provides information from the history of mathematics which helps to develop cognitive interest to the explored subject.