$\displaystyle \displaystyle A=\int_{-1}^0\int_0^{(x+1)^2}f(x,y) \ dy \ dx + \int_0^1\int_0^{(x-1)^2} f(x,y) \ dy \ dx

$

By reversing the order of integration, express A as a single iterated integral.

Would it be like this

$\displaystyle \displaystyle A=\int_{0}^1\int_{\sqrt{y}-1}^{0}f(x,y) \ dx \ dy + \int_0^1\int_0^{\sqrt{y}+1} f(x,y) \ dx \ dy$