Dear All!

Proof ofthe second fundamental theorem

Please, how do we get in the sixth line that f(x) is right the one f(t), also, the sam f function as we have in the lines before?

In other words, how do we KNOW that $\displaystyle (F(x+\Delta x)-F(x))=f(x)$ The SAME f(x) we have in the right side before?

I understand that it is an DERIVATIVE, SURE! "An derivative! " But how do we know it is the same FUNCTION as we have f(t) on the right?

Many thanks!