Difference expressed as integral of differential?

[bthongchai]

Difference expressed as integral of differential??

Hi all, I came across an equation in this form while trying to understand a paper:

f(t+T) - f(t) = \int_t^\(t+T\\frac{d}{dt} f(t') \, dt'

but I was unable to see how it can be true. If I bring the term \frac{d}{dt} outside of the definite integral, it seems to work, but I don't think that is allowed? Can anybody help? Thanks!

 

[g_edgar]

f(t+T) - f(t) = \int_t^\(t+T\\frac{d}{dt} f(t') \, dt'

I think it should be written with \frac{d}{dt'} inside, not \frac{d}{dt} .