Let $[a, b] \subseteq \mathbb{R}$ be a D544: Closed real interval such that
| (i) | $a < b$ |
| (ii) | $f : [a, b] \to \mathbb{R}$ is a D1760: Riemann integrable real function |
| (iii) | $F : [a, b] \to \mathbb{R}$ is a D5614: Differentiable real function on $(a, b)$ |
| (iv) | \begin{equation} \forall \, t \in (a, b) : F'(t) = f(t) \end{equation} |
| (v) | \begin{equation} x \in [a, b] \end{equation} |
Then
\begin{equation}
F(x)
= F(a) + \int^x_a f(t) \, d t
\end{equation}