An object is moved along the path $C$ parameterized by $\mathbf{r}(t) = \langle t^3, t^2 \rangle$ for $0 \le t \le 1$. If the force field is $\mathbf{F}(x,y) = \langle y, 0 \rangle$, write down the simplified single-variable integral with respect to $t$ that computes the work done.