Limits of integration with polar coordinates.

Ok, I have the following problem find the area inside the cardioid

$\displaystyle r = 1 -sin\theta$

and outside the circle

$\displaystyle r = \frac{1}{2}$

I know you check for the limits of integration by finding where the two graphs intersect which is

$\displaystyle \frac{\pi}{6} and \frac{5\pi}{6}$

However they show how the solution is done im a trying to re work it and they say you can just take the area of half the region and multiply it by two which gives the these limits of integration

$\displaystyle \frac{\pi}{6} and- \frac{\pi}{2}$

How the hell that came up? I cant see where the right half the graph starts at -pi/2