Polar double integral bounds help

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So I have the integral which needs to be computed :

$$I = \int_{-2}^{0} dx \int_{0}^{\sqrt{4-x^2}}(x^2+y^2)dy + \int_{0}^{\sqrt2} dx \int_{x}^{\sqrt{4-x^2}} (x^2+y^2)dy$$

and we're told to convert to polar coordinates and work out the solution

My question is about the integral bounds that are a bit tougher than usual. What I got are: $\frac{\pi}{4}< \theta < \pi$ and $0<r<2$

Which yields $I =3\pi$

I hope someone could either correct me and tell me how to do it.

Thank you!