Definition:Primitive (Calculus)

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

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