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

(i)	$$\begin{equation} a < b \end{equation}$$
(ii)	$f : [a, b] \to \mathbb{R}$ is a D1760: Riemann integrable real function

A D993: Real number $a \in \mathbb{R}$ is an arithmetic mean for $f$ if and only if $$\begin{equation} \int^b_a a \, d t = \int^b_a f(t) \, d t \end{equation}$$