fubini application on $\int_{0}^{1}\int_{-\sqrt{1-y^2}}^{\sqrt{1-y^2}}ydxdy$

Question

I have the integral $$\int_{0}^{1}\int_{-\sqrt{1-y^2}}^{\sqrt{1-y^2}}ydxdy$$

I am trying to apply fubini theorem, so I am trying to changes the interval of $x$ and $y$

I got to the result that $0<y<\sqrt{1-x^2}$ and $-1<x<1$

are those limits right? because I am not getting the same result.

I would like for an explnation about the attitude for this kind of problem