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integration is reverse of differentiation and vice versa
Integration and differentiation effectively un-do each other. The derivative of the integral of a function is usually the original function. The reverse is also true, to a point.
In basic terms, Calculus is Differentiation and Integration And all things associated with that.
An integral and an anti-derivative are the same thing. Integration means the process of finding the integral, just as anti-differentiation means the process of finding the anti-derivative.
Analysis can be thought of as a continuation of calculus. It deals with topics such as measure, limits, and integration/differentiation, and spaces (such as metric spaces).