If f'(x)=3x(x - 1), find f(x)

Due to notation difficulties, S = integral sign. This is a straightforward integration question, firstly we expand the brackets:

f'(x)=3x^2 - 3x f(x)=S(3x^2 - 3x)dx f(x)=3/3x^3 - 3/2x^2 + C f(x)=x^3 - 3/2x^2 + C

C is the constant of integration, the next part of the question would typically give the student a point through which this curve passes and then ask them to find the constant of integration.