is it correct to prove that way? if exists point c, so maintains:

so - rather the integral is negative and the fracture, or the integral is positive and so is the fracture. and, obviously we know the fracture is positive, so we can conclude that the integral is also positive.

can i do that? isn't that correct only when the function is continous?! or maybe because it's given that "f is continous in " it's fine?