#### Answer

The area is the region bounded by $r=1$, $r=2$, $\theta= \pi/6$ and $\theta= 5\pi/6$ which lies in first and second quadrants.The boundaries include $r=1$, $\theta= \pi/6$ and $\theta= 5\pi/6$ and exclude $r=2$.
This has been illustrated in the attached graph.