I am self-studying some probability for fun... I realised I have no idea how I would calculate P[X>Y] if X~N(0,1) and Y~U(0,1). Running simulations suggests the answer should be around 0.315, but I am looking for an integral form to compute the exact value.
I have tried $$\int_{-\infty}^{\infty}\int_{y}^{\infty}\frac{e^{-x^2/2}}{\sqrt{2\pi}}dxdy$$ but this doesn't seem to be giving me the correct values.