Definition:Primitive (Calculus)/Real

Definition
Let $F$ be a real function which is continuous on the closed interval $\left[{a \,.\,.\, b}\right]$ and differentiable on the open interval $\left({a \,.\,.\, b}\right)$.

Let $f$ be a real function which is continuous on the open interval $\left({a \,.\,.\, b}\right)$.

Let:
 * $\forall x \in \left({a \,.\,.\, b}\right): F' \left({x}\right) = f \left({x}\right)$

where $F'$ denotes the derivative of $F$ with respect to $x$.

Then $F$ is a primitive of $f$, and is denoted:
 * $\displaystyle F = \int f \left({x}\right) \, \mathrm d x$

Also known as
A primitive is also known as an antiderivative.

The term indefinite integral is also popular.