∫(a→x) (x - t)f'(t) dt
= ∫(a→x) (x - t) df(t)
= (x - t)f(t):(a→x) - ∫(a→x) f(t) d(x - t)
= (x - x)f(x) - (x - a)f(a) + ∫(a→x) f(t) dt
= (a - x)f(a) + ∫(a→x) f(t) dt
d/dx ∫(a→x) (x - t)f'(t) dt
= d/dx [(a - x)f(a) + ∫(a→x) f(t) dt]
= - f(a) + f(x) - 0
= f(x) - f(a)