\begin{definition}[Definition:Primitive (Calculus)/Real]
Let $F$ be a real function which is continuous on the closed interval $\closedint a b$ and differentiable on the open interval $\openint a b$.
Let $f$ be a real function which is continuous on the open interval $\openint a b$.
Let:
:$\forall x \in \openint a b: \map {F'} x = \map f x$
where $F'$ denotes the derivative of $F$ {{WRT|Differentiation}} $x$.
Then $F$ is '''a primitive of $f$''', and is denoted:
:$\ds F = \int \map f x \rd x$
\end{definition}