Help with a calculus proof

I need to prove that:

integral from 1 to a of 1/t dt + integral from 1 to b of 1/t dt = integral from 1 to ab of 1/t dt.

I am not allowed to use the fundamental theorem to solve this one. Just the properties of integrals and upper and lower sums.

If anyone could give me a hint as to where I should start with this one I would be extremely grateful

 

I'm only in geometry. I wish I could help you, though. Good luck