Integration Proof: Proving/Refuting |f(x)-g(x)| Integrable on [a,b]

[Rony]

Homework Statement

prove or refute : let f(x), g(x) be integrable functions on [a,b] so |f(x)-g(x)| integrable on a [a,b]

Homework Equations

The Attempt at a Solution

I'm pretty sure that it's right, I just can't find formal proof, someone can give me direction.

 

[Eynstone]

Welcome Rony,
Use the triangle inequality |f(x)-g(x)| <= |f|+|g| to prove finiteness & the fact that f-g can be approximated with the corresponding differences of step functions
approximating f & g.