Let $a_{x}$ and $a_{y}$ be unit vectors along $x$ and $y$ directions, respectively. A vector function is given by $$F=a_{x}y-a_{y}x$$
The line integral of the above function $$\int _{C}F.dl$$ along the curve $\textbf{C}$, which follows the parabola $y=x^{2}$ as shown below is ___________ (rounded off to $2$ decimal places).
