Correlated Expectation of Random Variables

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There are $2$ random variables $X\sim N(0,1)$ and $Y\sim N(0,1)$. These $2$ random variables are correlated, which can be given as $Corr(x,y) = \rho$

How do I compute an expectation of the below form?

$E[f(X) | Y > H]$ ?

$f(X)$ - It's a function of $X$.

$Y > H$ is a condition for computing the expectation. $H$ is a constant

How should I go about this?

If the condition did not exist I could have written this in the Integration Form. But with the condition how do I do that?