area of overlap between two curves

${\int }_a^b(\mathrm{upper}\mathrm{curve}-\mathrm{lower}\mathrm{curve})dx$

or (if the curve equations are in terms of $y$, i.e. $x=\dots$)

${\int }_a^b(\mathrm{right}\mathrm{curve}-\mathrm{left}\mathrm{curve})dy$