Lets check to see if your anti-derivative is correct. To do this, we derive your answer, and we should get back the original problem.
d/dx(3x4 - 3x3 + 4x2 - 3x + 7) =
12x3 - 9x2 + 8x - 3
Your anti-derivative is good, but just replace the 7 with C , since C is any arbitrary constant.