\(\text{For this problem I would choose }\\ x=f(t) = t^2,~y=g(t) = t\\ \text{Then }\textbf{dx}=(2t,1)dt\\ \textbf{F(x)$\cdot$ dx}= (t^4,t^2)\cdot (2t,1)dt =2 t^5+t^2~dt\)

I leave you to complete the final integral

\(\displaystyle \int_0^3 2t^5+t^2 ~dt\)

.