U-substitution is exactly the way to go.
First off, you have:
Now, let
, so that
. Then
.
Put this all back into the original integral, factoring out the -1/3 since it's a constant. This leaves you with:
Integrating that with respect to u gives you this (don't forget to multiply through by the -1/3):
Now replace the u with 6 - 3x, giving you a final answer of:
That's all.