lim(x->a) [x/(x-a)] ∫[a,x] f(t)dt
=lim(x->a)[a/(x-a)]∫[a,x]f(t)dt +lim(x->a)∫[a,x]f(t)dt
=lim(x->a) a*[∫[a,x]f(t)dt]'/(x-a)'
=lim(x->a)a*f(x)
=af(a)
lim(x->a) [x/(x-a)] ∫[a,x] f(t)dt
=lim(x->a)[a/(x-a)]∫[a,x]f(t)dt +lim(x->a)∫[a,x]f(t)dt
=lim(x->a) a*[∫[a,x]f(t)dt]'/(x-a)'
=lim(x->a)a*f(x)
=af(a)