I don't see why these two equations should be different, but they return different values.
Integrate[Sin(2x)*D[DiracDelta(3x),x],{x,-1,1}] = -2/3
Integrate[Sin(2x)*DiracDelta'(3x),{x,-1,1}] = -2/9
When I do the problem by hand I find that the second answer of -2/9 to be the correct one. Am I misunderstanding the notation of D and ' or is this a bug?