The first integral is :
The y limits state that
Now, the region can be expressed , which is a circle of radius 2 with its center at the original, and the region is a straight line in line with the x axis! So in the y axis, the region is bounded between the x axis, and the circle described.
And the x axis limits are x = 0 and x = 2. So I'm sure you can understand what this means!