Given that the equation of the curve y=f(x) passes through the point (-1,0), find f(x) when f'(x)= 12x^2 - 8x +1

Firstly, Integrate the f'(x) equation by raising the power by 1 and then dividing by the new power and adding a constant c. This gives you f(x)=(12x^3)/3 -(8x^2)/2 + x + c Then you simplify, f(x)=4x^3 -4x^2 + x + c Insert your y and x values to find c, 0= 4(-1) - 4(1) -1 + c Therefore c= 9 and f(x)= 4x^3 -4x^2 + x + 9