# Difference expressed as integral of differential?

## Main Question or Discussion Point

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!

$$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 $$\frac{d}{dt}$$ .