13.2#14

Can you tell me what I'm doing wrong for part B?

Well, it's hard for me to tell how you got that answer, because it's pretty far off. You need to understand the definition of line integral: since you are given a particular vector field, you need to do the line integral of that vector field, along the curve you have, which looks like the following:

Next you have to use the parameterization you already wrote down x(t)=t, y(t)=t^2, which will give you x'(t)=1 and y'(t)=2t, hence you have:

 
which gives you