Vector Calculus · Medium problem

A triangular metal plate has vertices at $(0,0)$, $(1,0)$, and $(1,k)$, for some unknown $k>0$. A fluid with velocity field $\mathbf F=(xy,\,x^2)$ circulates around the boundary of the plate, traversed counterclockwise. If the total circulation $\displaystyle\oint_C xy\,dx+x^2\,dy$ around the boundary equals $1$, find $k$.