Let’s talk about the relationship between limits, derivatives, differentials, definite integrals, variable upper limit integrals, and indefinite integrals.

Limits are the basis of the entire calculus, and all concepts of calculus are based on limits.

In a one-variable function, differentiability and differentiability are equivalent.

The indefinite integral is the inverse operation of the derivative operation.

The definition of definite integral is the limit of the sum of integrals. The original meaning is a limit problem; however, the derivative of the integral with a variable upper limit (that is, the integral function) is the integrand. Therefore, the definite integral problem is also about finding the original Function problem, in this way, differential and integral are a pair of mutually inverse operations.