Suppose $\mathbb{G}$ is a tight zero mean Gaussian process and $F$ is an absolutely continuous CDF
$$Y=\int_a^b\frac{d\mathbb{G}}{1-F}+\int_a^b\frac{\mathbb{G} \, dF}{(1-F)^2}$$
I know that $Y$ is a normal random variable. However, the question is how do I derive its mean and variance?
Thank's!