am I on the right track here?
Yes. I would write:
edit: Don't forget the differential in your definite integral and avoid using a rounded decimal approximation (at least if you have the same professor I did).
That's fine. You can check this sort of thing here integral (-2,6) (x+3)^(1/2) dx - Wolfram|Alpha
EDIT: Oh nevermind. I get it now.