I need help setting up the integral so that I can calculate the work done. I've tried it many times and have referred to Youtube, slader, the textbook, and also this site, but I still don't get how to solve it. I came up with a few solutions but they were all wrong. Please help, I've been at this for 2 hours.
Your $P(x)$ is wrong because you took the base to be the top face, presumably because it is larger than the bottom face. The base is the bottom face. Instead of $5-(2/3)x$ it should be $3+(2/3)x$. Good on you for using parentheses. I didn't do the second part.