If there is an area between 2 curves and it's spun around the x-axis I integrate with respect to x, else if it's spun around the y-axis I integrate with respect to y. What screws me up is finding the area because I subtract the wrong function. For example, $\displaystyle y^2=x$ and $\displaystyle 2y=x$. The $\displaystyle y^2$ is on top but the $\displaystyle 2x$ is to the right.

Which rule takes precedence; right-left or top-bottom?

If I get a negative volume, chances are I have the functions switched around, but the converse isn't always true right? For example I could still have the the functions switched around and still get a positive answer?