Use completing the square to get the 2nd equation into a workable format!

So now you have a circle centred at the origin with a radius of two, given by the first equation, and a circle centred at the point (1,0) with a radius of 1. Draw these, and see if the image makes it easier you to visualise the integral.

Although I'm not sure what they mean by the 'area that lies between the circles', because there is no area BETWEEN them... one circle is inside the other.