I am trying to understand the proof of every monotonic function that is on an interval is integrable.
This is what I have $U(f, P) - L(f, P) = \sum\limits_{k=1}^n(f(t_k) - f(t_{k-1}))\cdot (t_k - t_{k-1})$
Now my book says that this is equal to:
$= (f(b) - f(a))\cdot(t_k - t_{k-1})$
How does one deduce that $\sum\limits_{k=1}^n(f(t_k) - f(t_{k-1})) = f(b) - f(a)$?