10. (10 Points) Evaluate the line integral $\int_C (ye^x+\sin y)\,dx+(e^x+x\cos y)\,dy$ along the curve $C:r(t)=(t^2+1)\mathbf{i}+(t^2-1)\mathbf{j},\ 0\le t\le 2$. Hint: you may find a potential function $f$ of the vector field $F(x,y)=(ye^x+\sin y)\mathbf{i}+(e^x+x\cos y)\mathbf{j}$, i.e. find $f$ so that $F=\nabla f$.