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

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

Then

(1)	$[a, c] \to \mathbb{R}, \quad x \mapsto f(x)$ is a D1760: Riemann integrable real function
(2)	$[c, b] \to \mathbb{R}, \quad x \mapsto f(x)$ is a D1760: Riemann integrable real function
(3)	\begin{equation} \int^b_a f(x) \, d x = \int^b_c f(x) \, d x + \int^c_a f(x) \, d x \end{equation}