Work = area under Force vs distance curve

Just as we found the displacement was the area under the velocity vs time curve, we can use the same reasoning to show work is the area under the force vs distance curve.

In other words:
Since W = F x d (provided d and F are in the same direction) if we look at a strip of area under the force curve. That strip of area is F high and delta distance wide; so it has an area of F x delta distance. This is the work done over the delta distance. If we add up all these strips we get the work done for all the delta distances which is the work done for the total distance.