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 $\left({a \,.\,.\, b}\right)$.

Suppose that:
 * $\forall x \in \left({a \,.\,.\, b}\right): F^{\prime} \left({x}\right) = f \left({x}\right)$

where $F^{\prime}$ signifies the derivative of $F$.

Then $F$ is known as a primitive (or an antiderivative) of $f$.