Reversal of Limits of Definite Integral

Theorem
Let $\left[{a \,.\,.\, b}\right]$ be a closed real interval.

Let $f: \left[{a \,.\,.\, b}\right] \to \R$ be a bounded real function.

Let:
 * $\displaystyle \int_a^b f \left({x}\right) \rd x$

be the definite integral of $f$ over $\left[{a \,.\,.\, b}\right]$.

Let $a > b$.

Then:
 * $\displaystyle \int_a^b f \left({x}\right) \rd x := - \int_b^a f \left({x}\right) \rd x$