Find the area between $r = 1 - \sin θ$ and the circle $r = \sin θ$? I have found the points of intersection but am not sure how I would split this into two integrals or why?
As you can see from Desmos, if you want the area between both we can do a little bit of symmetry to just get the area of one of the lobes, giving us
$$I = 2\cdot\frac{1}{2}\int\limits_{\text{first lobe}} r^2\:d\theta = \int_0^{\frac{\pi}{6}}\sin^2\theta\:d\theta + \int_{\frac{\pi}{6}}^{\frac{\pi}{2}}(1-\sin\theta)^2\:d\theta$$
from looking at the bounds in the picture. Can you take it from here?
Use polar coordinates $x=r\cos(\theta)$ and $y=r\sin(\theta)$ to change your problem to Cartesian coordinates. Then you can use a geometrical approach, even integration, to find the number.
Edit: You could try making graphs on dependent variable $r$ for independent variable $\theta$ without going to Cartesian (since the equations are so simple).