Get f(x | y) from this thread: http://www.mathhelpforum.com/math-he...-question.html
by substituting the rule for f(x, y). Then substitute y = 1/2 to get f(x | y = 1/2).
Then $\displaystyle \Pr(X < Y | Y = 1/2) = \int_{x = -1}^{x = 1/2} f(x \,| \, y = 1/2 ) \, dx$.
But given the careless mistakes I've made in two threads related to this question (forgetting about -1 < x < 0), you might want to check this carefully.