ThmDex – An index of mathematical definitions, results, and conjectures.
Real Riemann integral over a reflected interval
Formulation 0
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 on $[a, b]$
Then \begin{equation} \int^b_a f(x) \, d x = \int^{-a}_{-b} f(-x) \, d x \end{equation}