ON THE CONCEPT OF INTEGRAL, HISTORY OF ORIGIN AND SOME COUNTER-EXAMPLES

In the article is given  information about the integral concept and the history of its origin. In addition to the Riemann integral, which is covered in the school program, a number of other integrals (Riemann-Stiltes, Daniell, Alfred Haar, Henstock-Kurzweil, Ito and Stratonovich, Chokvet) are described. The difference between integrals is explained with the help of specific examples. The concept of definite integral and its use in practical problems were explained in detail, counter-examples of some theorems were presented.