One fundamental problem encountered when effectively teaching mathematics to students of economics is communication with learners that lack an adequate background. In the past, more than 66 per cent of freshmen enrolled at one of the faculties of our university did not take their school-leaving examinations in mathematics, even at the elementary level. One method to encourage students to better learning includes the examples of areas in economics where they can apply mathematical concepts. Usually, the course in mathematics is relatively short and offered in the first semester, therefore it is not quite easy to actually introduce necessary economic concepts, even if only intuitively. Nevertheless it is worth trying. The paper gives several simple and useful examples of an integral's applications in economics, such as estimating resources based on the intensity function of a flow; calculating a consumer's surplus; the time value of capital; comparing levels of social wealth.