Refer to the image for the region. I've chosen to "scan" the region horizontally for convenience sake, so x varies for values between the green and the red line, and y varies from 0 to 1.
The two lines have equations (red line) and (green line). Since we're integrating first with respect to x, it's easier to write the equation like that and not as since they will become our new limits of integration
Our double integral will become