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 D4364: Real function |
| (iii) | \begin{equation} \exists \, \lambda \in \mathbb{R} : \forall \, x \in [a, b] : f(x) = \lambda \end{equation} |
Then
| (1) | $f$ is a D1760: Riemann integrable real function |
| (2) | \begin{equation} \int^b_a f(x) \, d x = \lambda (b - a) \end{equation} |