Suppose I have that:
$ \gamma = \int_{a_1}^{a_2} \int_{b_3}^{g(y)}h(x,y)dxdy + \int_{a_2}^{a_3} \int_{b_3}^{b_4}h(x,y)dxdy + \int_{a_3}^{a_4} \int_{f(y)}^{b_3}h(x,y)dxdy + \int_{a_4}^{a_5} \int_{b_2}^{b_3}h(x,y)dxdy$
But, suppose it is also the case that $g(a_2)=b_4$ and $f(a_4)=b_2$
Can I then rewrite the integral as
$ \gamma = \int_{a_1}^{a_5} \int_{b_1}^{b_4}h(x,y)dxdy$ ?
Or is it only correct to say
$ \gamma = \int_{a_1}^{a_3} \int_{b_3}^{b_4}h(x,y)dxdy+ \int_{a_3}^{a_5} \int_{b_2}^{b_3}h(x,y)dxdy$ ?
Or neither?