Ok I am pretty sure what I have done is correct various things are telling me wrong so can someone tell me where I went wrong and the correct way to do it. Thanks.

dA = (top-bottom) dx

= (x^3-12x^2+20x)-(-x^3+12x^2-20x) dx

= (2x^3-24x^2+40x) dx

therefore..

∫ (2x^3-24x^2+40x) dx from x=0 to x=2

{(1/2)x^4-8x^3+20x^2} from x=0 to x=2

therefore..

((1/2)(2)^4-8(2)^3+20(2)^2) - 0

= 24

this seems to be incorrect so can someone explain to me why and how to correctly do it? Thanks