Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

x+y=2

x=3–(y–1)^2

about the x-axis.

What I did was solve for x for both equations and made them equal to each other and tried to find the points of intersection, but I don't think i'm doing it correctly. Can someone elaborate on what I should do and the steps involved.

I'm not sure on whether to apply the shell or disc method to find the answer as well.

I'm also confused as to when it says, for example, "about the x-axis." Do I solve looking for y or x?

Thank you.