The intuitive derivation for the integrated form of the Kolmogorov backward equation makes sense and is given in the Act Ed notes on page 17 and 18. However, if I use the same logic when deriving the integrated form of the Kolmogorov forward equation I get a different equation from the notes.

My attempt is uploaded here: http://imgur.com/hGzy1fu

I am trying to follow the logic used in the backward case, noting that I change the focus from the first jump to the last jump.

Please help

Thanks for the response. I've looked over the full proof and it makes sense so my derivation was definitely wrong. Points 1 and 2 specifically were incorrect and I've figured out what I need to fix