Reversal of Limits of Definite Integral

Theorem
Let $\closedint a b$ be a closed real interval.

Let $f: \closedint a b \to \R$ be an integrable real function.

Let:
 * $\ds \int_a^b \map f x \rd x$

be the definite integral of $f$ over $\closedint a b$.

Let $a \le b$.

Then:
 * $\ds \int_a^b \map f x \rd x = -\int_b^a \map f x \rd x$