draw the curves, to see how it looks (looks like a moon)

then calculate where the curves meet (set r=r, calculate phi1 and phi2, insert phi into the equation and calculate r1 and r2)

then integrate from r1 to r2 and from phi1 to phi2, using

area=integral r*dr*dphi

edit: sorry, my wrong. It's two circles one inside the other, one has radius 3/2 the other 1/2, so the area should be

pi*(9/4 - 1/4) = pi*2