Find the area of the surface generated when the arc of the curve between y = 0 and y = 1 is revolved around (a) the y-axis, (b) the x-axis, and (c) the line y = -1.

I am stuck on the first one and thought that I should figure out what I am not getting before I press on. My answer keeps comming up negative, and I can't figure out why. Here is what I have:

Inverting the limits of integration (integrating from 1 to 0 instead of from 0 to 1) would make the answer positive, but is there a reason to do that? I so, could you explain why? Or is there some other mistake I am making? Like I said, I would like to get this sorted before I go on to the other problems. (I am not looking for help on the other parts -- b and c -- of the problem at this point, except for some general guidance, especially relative to what ever mistake I am making in this problem.)