Consider the integral $\displaystyle \int_0^3 \int_0^{\sqrt{9-y}} f(x,y) dx dy$. If we change the order of integration we obtain the sum of two integrals:

$\displaystyle \int_a^b \int_{g_1(x)}^{g_2(x)} f(x,y) dy dx + \displaystyle \int_c^d \int_{g_3(x)}^{g_4(x)} f(x,y) dy dx$
$a =$ $b =$
$g_1(x) =$ $g_2(x) =$
$c =$ $d =$
$g_3(x) =$ $g_4(x) =$