I have the following:
The sum of the iterated integrals $$ \int_{-2}^{-1}\int_{-\sqrt{y+2}}^{\sqrt{y+2}} f(x,y)\, dx\, dy + \int_{-1}^{2}\int_{y}^{\sqrt{y+2}} f(x,y)\, dx\, dy$$ is equal to:
a) $\int_{-1}^{\sqrt{2}}\int_{x^2+1}^{x-1} f(x,y)\, dy\, dx$
b) $\int_{-1}^{2}\int_{x^2-2}^{x} f(x,y)\, dy\, dx$
c) $\int_{-\sqrt{2}}^{2}\int_{x^2-2}^{x} f(x,y)\, dy\, dx$
d) $\int_{-2}^{2}\int_{x^2+2}^{x} f(x,y)\, dy\, dx$
e) $\int_{-\sqrt{2}}^{\sqrt{2}}\int_{x^2+2}^{x} f(x,y)\, dy\, dx$
I'm not sure how to combine the sums to be honest. The answer isn't choice D. If this was a single integral, I can change the bounds more easily, but with something like this, I am not so sure... I assume the bounds are in some kind of circle but I am not sure.
How do I combine this to a single integral?