Integration help needed C2

Find the equation of the curve which passes through the point (-1,0) andwhose gradient at any (x,y) is $3x^{2}-6x+4$. Find the area enclosed by the curve, the axis of x and the ordinates x=1 and x=2.


Please help with the question. I cant find the equation. I am struggling to find a way to.

What information is it giving you in the question so that you can find f(x)?

I have atteched the workings I did but I still got it wrong the book says the equation of the curve is $x^{3}-3x^{2}+4x+8$
please help

Find the equation of the curve which passes through the point (-1,0) andwhose gradient at any (x,y) is $3x^{2}-6x+4$. Find the area enclosed by the curve, the axis of x and the ordinates x=1 and x=2.


Please help with the question. I cant find the equation. I am struggling to find a way to.

y=13x+1 is not equal to to the equation of the curve - you've found the equation of the tangent to the curve at the point (-1,0), but the question doesn't require you to find that.

You have integrated correctly to find the equation of the curve, so how can you find the value of c?