# Reversal of Limits of Definite Integral

## Theorem

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

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

Let:

$\displaystyle \int_a^b \map f x \rd x$

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

Let $a > b$.

Then:

$\displaystyle \int_a^b \map f x \rd x := - \int_b^a \map f x$