Could someone explain in a bit more detail the move from 26 to 27? I don't get the significance of being "worried about optimization" or why/how we cancel p(x). I do get the later point about integration and the convenience of the reformulation. I just don't get why or how it is "allowed".

Sorry if this is obvious but I have been doing a lot of reading on this and have come across this step a few times before...but am just missing some part of every explanation.