f_n(x)=f_n(a)+∫[a,x]f'_n(t)dt
→f(x)=f(a)+∫[a,x]g(t)dt (n→∞) (∵f'_n→g:unif)
||f_n-f||=sup|f_n(a)-f(a)+∫[a,x]f'_n(t)-g(t)dt|
≤|f_n(a)-f(a)|+sup|∫[a,x]f'_n(t)-g(t)dt|
≤|f_n(a)-f(a)|+sup{∫[a,x]|f'_n(t)-g(t)|dt}
≤|f_n(a)-f(a)|+∫[a,b]|f'_n(t)-g(t)|dt
≤|f_n(a)-f(a)|+(b-a)||f'_n-g||→0 (n→∞)
