H$4\mathrm{.}3$ Line integral $-$ work done by a $2$D force:

A particle moving in the $x-y$ plane is subject to a force

vec$(F)(x,y)=(25N{m}^2)\frac{\text{x}\text{v}\text{e}\text{c}(e{)}_x+\text{y}\text{v}\text{e}\text{c}(e{)}_y}{(x^2+y^2{)}^{\frac{3}{2}}}$

where $x$ and $y$ are measured in meters $(m).$ Calculate the work done on the particle by this force, as it moves along the parabolic trajectory $y(x)$ given by the unitless expression $y\frac{x}{m}=(\frac{x}{m}{)}^2-2\frac{x}{m}+3$ from the point $(1\mathrm{.}0m,y(1\mathrm{.}0m))$ to the point $(3\mathrm{.}0m,y(3\mathrm{.}0m)).$