1. The meaning of definite integral: definite integral is a kind of integral, which is the limit of the integral sum of function f(x) in the interval [a, b].

2. Here, we should pay attention to the relationship between definite integral and indefinite integral: if definite integral exists, it is a concrete numerical value, while indefinite integral is a functional expression, and they have only one mathematical relationship (Newton-Leibniz formula).

3. The definition of function is usually divided into traditional definition and modern definition. The two definitions of functions are essentially the same, but the starting point of describing concepts is different. The traditional definition is from the perspective of movement change, and the modern definition is from the perspective of set and mapping.

4. The modern definition of a function is to give a set of numbers A, assume that the element in it is X, apply the corresponding rule F to the element X in A, and record it as f(x) to get another set of numbers B, assume that the element in B is Y, and the equivalent relationship between Y and X can be expressed as y=f(x). The concept of function consists of three elements: domain A, domain B and corresponding rule F..

5. The core is the correspondence rule F, which is the essential feature of the functional relationship.