This must be a classical problem, but I don't know where to start. I have a simple (actually it's more complicated, but essentially like this) integral: . It seems that the function x(t) could be best described as a normal (Gaussian) process with mean mu and some variance (so x(t) is a random variable with Gaussian distribution). I think y(t) must then be also a random variable, but is there any way to define y(t) in a closed form? Or is this problem reasonable at all? How should I continue? Thanks for your help!