Yeah, only subtract the two equations if you need to find the area between them.
As for splitting the integral up, you only need to do this if your graph crosses the x-axis (if working with an area bound by the x-axis) since once it crosses the x-axis, the area is negative and anything you calculate will just cancel out what you've calculated in positive area. A good example of this is the sine wave. If you want to find the area bound by the equation y=sinx and the x-axis in the domain between 0 and 2pi, you would get 0 if you didn't split the integral. Splitting it where ever it crosses the x-axis will get you your answer. So in this example, you find the integral of sinx twice, between 0 and pi, and then between pi and 2pi - then add the two integrals together. Be careful with the second integral though, it may turn out negative. If it does, make it an absolute value since you can't have negative area!
Volume of rotation is pretty simple once you get you get used to it. Just remember the formulas and apply what rules you normally would when finding normal integration areas. Once again, only split it up if it cuts the axis that it's being bound by or rotated around.
