Proving and calculation an integral from the definition

Hello

I have the following problem: given that f : [a,b] > R is integrable, prove that

g = f/2 is integrable and find the integral.

I'm learning Darboux integrals, so my instinct is to try and calculate the upper and lower sums of g and show that for all epsilon, there exists a partition of [a,b] such that the difference between them is less than epsilon...but I'm not sure how I can break apart the difference in order to use the fact that f is integrable...i'm very confused.