What is the area of the region inside the limacon with equation $r=3+2 \sin (\theta)$ that lies below the line $y=x$? What is the area of the region inside the limacon with equation $r=3+2 \sin (\theta)$ that lies below the line $y=x$?

I know I should use Riemann sum but how to write the equation?  And what about the $y=x$?


Notice that, as mentioned in the comments as well, the line is a combination of the rays corresponding to $\displaystyle \theta = \frac{π}{4}$ and $\displaystyle \theta = -\frac{3π}{4}$.
Just reminding you, polar curves are traced out by angle, and so are their integrals. 
We have that the area enclosed by the two rays $\theta=a$ and $\theta=b$, the origin, and $r=f(\theta)$ is $\displaystyle \frac{1}{2}\int_a^b f(\theta)^2 \,d\theta$.
We have the rays $\displaystyle \theta = \frac{π}{4}$ and $\displaystyle \theta = -\frac{3π}{4}$ and $r=f(\theta)=3+2\sin(\theta)$.
We have $\displaystyle \frac{1}{2}\int_{-\frac{3π}{4}}^{\frac{π}{4}}(3+2\sin(\theta))^2\,d\theta=\boxed{\frac{11π}{2}-6\sqrt{2}}$ units$^2$.
