Calculus knowledge points

I don’t understand this Calculus question and need help to study.

List knowledge points are defined mathematically. And give some example to help explain the question. The knowledge points can be pictures or words. The questions used in the examples cannot be the most basic, and relatively difficult. Need to be in the form of pictures. It’s best to have different small details in one content, examples.

Integrals

-areas and distances

-definite integral

-fundamental theorem of calculus

-antiderivative

-substitution rules

-approximate integration

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