Reversal of Limits of Definite Integral

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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:

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


Proof


Sources