Ignore the middle term in the answer. The area from -5 to -3 is (the area from -5 to -2 ) - (area from -3 to -2). There is no ambiguity here.
in the above example when it says that you can add the integral from -2 to -5 TO the integral from -2 to -3, would it not double count the area between -2 and -3?
similar to an intersection of sets when you have A union B you have to minus A intersect B to get the correct area. Why does that idea not pertain to integrals? Or does it?