swapping limits of integration in definite integral

for interval $[a, b]$ ,

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x

PROOF/

\int_{a}^{b} f (x) d x = F (b) - F (a)

and

\int_{b}^{a} f (x) d x = F (a) - F (b) = - 1 (F (b) - F (a)) = - \int_{b}^{a} f (x) d x

QED