Let $f$ be continous on $[a,b]$ and differentiable a.e. on $(a,b)$. Suppose there is a non-negative
function $g$ integrable on $[a,b]$ and $|\displaystyle \frac{f(x+1/n)-f(x)}{1/n}|\leq g$ a.e on $[a,b]$ for all $n$.
How can I show that: $\quad\displaystyle\int_a^bf'=f(b)-f(a). $