You have to divide the question into two parts.
First, use integration to find the area under OA.
The, find the area of the triangle.
Then add them to gether.
![\int_{0}^{2}x^3-8x^2+20x](https://studentforums.biz/cgi-bin/mimetex.cgi?\int_{0}^{2}x^3-8x^2+20x)
Then find the area of the triangle:
![\frac{1}{2}(x_b-x_a)y_a](https://studentforums.biz/cgi-bin/mimetex.cgi?\frac{1}{2}(x_b-x_a)y_a)
That comes to:
![\frac{1}{2}(\frac{10}{3}-2)16](https://studentforums.biz/cgi-bin/mimetex.cgi?\frac{1}{2}(\frac{10}{3}-2)16)
As
![f(2)=16](https://studentforums.biz/cgi-bin/mimetex.cgi?f(2)=16)
So when you add them together, you get
![\frac{100}{3}](https://studentforums.biz/cgi-bin/mimetex.cgi?\frac{100}{3})