With mathematics it is possible to solve problems abstractly. That is, we don't need to know what the values mean. We just need to know the method that is used to relate one value to another. Calculus is a branch of mathematics that we use to describe the behavior of functions. We make that determination by differentiating the function.
Derivatives represent a rate of change.
This information allows us to draw a graph of the function and to describe its behavior. Integral calculus is used to determine which function, if any, changes in a specified manner. We make this determination by trying to find a function that, when differentiated, yields the specified function. This is called integration. This is not a single function but rather an entire family of functions with the desired property.