EDIT: Please excuse my typo, I meant integrate from 1 to 5.
Since you are rotating around the axis, this will be a integral.
The graphs intersect where the equations are equal...
When , so they intersect at .
The volume is calculated by rotating the area around the axis.
This area needs to be thought of as a series of rectangles, which when rotated, become cylinders.
The length of each rectangle is and the width is , a small change in .
When rotated, each cylinder has a radius the same as the length of each rectangle, so the circular cross-sectional area is . The height of each cylinder is the same as the width of each rectangle, .
Therefore the volume of each cylinder is .
So the entire volume can be approximated by , and when you increase the number of cylinders, this sum converges on an integral and the approximation becomes exact.
Thank you again for helping me with this type of problem. I'm glad you didn't get confused at the beginning where it said x = 1 + y^2 y = x - 3. The comma I typed in somehow became a superscript so it didn't separate the two equations. The corrected way should be x = 1 + y^2, y = x - 3 but it doesn't matter because you got the equation right anyways. Kudos to you.