integral

Make use of

$\int _{ a }^{ b }{ \left( f\left( x \right) \right) dx } +\int _{ f^{ -1 }\left( a \right) }^{ f^{ -1 }\left( b \right) }{ f^{ -1 }\left( x \right) dx } =bf\left( b \right) -af\left( a \right)$