then the integral of f'(x) with respect to x is ∫f'(x) dx = f(x)

Integration finds the accumulated change to retrieve the original function

A function F(x) whose derivative is equal to f(x), representing the inverse operation of differentiation

Integration of a derivative yields the antiderivative

Finding the cumulative sum or total accumulation of a function over a specified interval

Substitution, integration by parts, partial fractions, and trigonometric identities, depending on the complexity of the function

Finding the area under the curve of a function within a given interval

Physics, engineering, economics, and biology, where it is used to calculate quantities such as displacement, work done, volume, and area