this is a past exam. i will post a couple others later. thanks.
you have to remember that the integral gives the area "under" the curve (if the curve is under the x-axis, we interpret it as a negative area). draw vertical lines through x = -1 and x = 2. you need to find and sum the areas of all the figures bounded by the graph and the x-axis. this amounts to finding the area of rectangles and triangles, so it should be no big deal for you. remember you take the area to be negative for figures under the x-axis