No need for an integral, you can just use elementary geometry.

First, it helps to write the circles in general form...

, which has radius 6 units centred at the origin, and .

The second can be rewritten as

.

So it has radius 3 units centred at (3, 0).

By drawing a graph of the situation, you have the required region as a quarter of the larger circle minus half of the smaller circle.

So