This problem shows a graph. Its a line with points (-1.5,0), (-0.5,1), (0,1.5) and keeps going both ways.

It says that this is the derivative of f(x) and that it wants to know the area bounded between f(X) over interval [-2,1] given that f(0) = 1

So I got y=1x+1.5 as the equation of the line of the derivative.

f(x) = 1/2 x^2 + 3/2x + 1 (since f(0) = 1)

integral of f(x) = 1/6 x^3 + 3/4 x^2 + x + c

then the integral is between 1 and -2 so it becomes :

1/6+3/4+1+c - (1/6(-2^3) + 3/4(-2^2) + -2 + c) =

1/6+3/4+1+c +8/6 -12/4 +2 +c = 9/4

Problem is the answer is supposed to be 29/12

what am I doing wrong here?

(to describe the graph, its a straight line going up and to the right. definite points are (-1.5,0) and (0,1.5). I got the slope and figured out that the other points I said before were there (they look right also). Integrals I did seem right. I dont get it.