Let $I \subseteq \mathbb{R}$ be a D1284: Real interval such that
| (i) | \begin{equation} \text{Vol}(I) < \infty \end{equation} |
| (ii) | $f : I \to \mathbb{R}$ is a D5231: Standard-continuous real function |
| (iii) | $f$ is a D3238: Constant-bounded function |
Then $f$ is a D1760: Riemann integrable real function on $I$.