Since are rotating around the x-axis, and want to use "cylindical shells", you will want to integrate with resect to y.

The integral will be where "r" is the radius of the cylinder- that will be just "y", the distance from the x-axis to the line that, rotated around the x-axis, creates the cylinder, and "h" is the length of cylinder, the length of the line that creates the cylinder- that will be "1- x" where x is the x-coordinate of the point (x, y) at the left end of that line: since , x= ?