How do I find the region of integration (in cartesian coordinates) of the following integral? I need to define the integral
$$\iint_Rxdydx,$$
where the region $R$ is represented by the following graph:

I understand x must limited as: $0\le x\le1$, but I'm not sure how y is limited.
I tried limiting it as: $-x\le y\le\sqrt{1-x^2}$, because following the equation of the circle, $x^2+y^2\le1^2$, but wolfram is giving the following representation:

, which is not correct. What is the correct region of integration?

Mit den Kreiskoordinaten $x=r\cdot cos\phi;y=r\cdot sin\phi$ und dem Flächenelement $dxdy=rdrd\phi$ ergibt das: $\int_{\phi=-\frac{\pi}{4}}^{\frac{\pi}{2}}\int_{r=0}^1 rcos\phi drd\phi$
