An indefinite integral is the reverse process of differentiation. It represents a family of functions that have the same derivative.
The definite integral calculates the exact area under a curve between two points.
An antiderivative is another term for an indefinite integral. It represents a family of functions that have the same derivative.
This theorem connects differentiation and integration by stating that if F(x) is an antiderivative of f(x), then ∫f(x) dx from a to b equals F(b) - F(a).