My continuous-time, continuous step Stochastic Process P runs from time $t=0$ to $t=t_f$ and generates a path. I am able to observe its starting and ending position (so $P(0)=a$ and $P(t_f)=b$), but I'm unsure what happened in the middle. I want to come up with a PDF for the integral of the process from $0$ to $t_f$.
Any advice?