How do I find the area of the region bounded by the graphs of the given equations?

y=x+20; y=x^2

2 answers

The graphs intersect at (-4,20) and (5,25)

So, consider the area as a bunch of thin strips, each of width dx, and height equal to the distance between the curves. The area is thus

∫[-4,5] (x+20)-x^2 dx
= 1/2 x^2 + 20x - 1/3 x^3 [-4,5]
= 243/2
How do you get the [-4,5], I don't understand where those numbers come from?