Abstract: Curricular ideological and political education is an important way for colleges and universities to implement the fundamental task of morality establisnemnt and talent cultivation. Mathematical Analysis is the core course of mathematics major. Integrating ideological and political content into curriculum teaching can effectively accomplish the goal of educating people in mathematics. The calculation of definite integral is the key content of mathematical analysis course, which incoporates rich ideological and political elements. Therefore, taking "interval reproduction formula" as an example, the teaching mode of "Guidance, Lecture, Evaluation and Research" is expanded; the teaching concepts, teaching contents, teaching models and homework design are innovated, and the ideological and political elements of the course are integrated into the teaching links such as introduction, comment and summary, so as to improve students’ cultural self-confidence and innovative spirit, and to cultivate mathematical talents with both ability and political integrity.