If $\displaystyle f(x,y) = \frac{6}{7} \left(x^{2} + \frac{xy}{2}\right), \ 0<x<1, \ 0<y<2 $ then does $\displaystyle P\left(Y > \frac{1}{2} | X < \frac{1}{2}\right) = \frac{6}{7} \int\limits_{0}^{\frac{1}{2}} \int\limits_{\frac{1}{2}}^{2} x^{2} + \frac{xy}{2} \ dy \ dx $?