Let $[a, b] \subseteq \mathbb{R}$ be a D544: Closed real interval such that

(i)	$M = ([a, b], \mathcal{L}, \ell)$ is a D5108: Lebesgue submeasure space
(ii)	$f : [a, b] \to \mathbb{R}$ is a D1760: Riemann integrable real function

Then \begin{equation} \int^b_a f(x) \, d x = \int_{[a, b]} f(x) \, \ell(d x) \end{equation}