My question is from Folland "Real Analysis" 2nd ed. p.77 Chapter 2, #56.

If f is lebesgue integrable on (0,a) and

g(x) = integral (from x to a) [t^-1 f(t)dt]

Prove then that:

1. g is integrable on (0,a) and

2. integral (from 0 to a) [g(x)dx] = integral (from 0 to a) [f(x)dx]