Proving Integrability of Constant Function f on [a,b]

[tomboi03]

Suppose that f is integrable on [a,b]. Let c E $$\Re$$. Prove that cf is integrable on [a,b] and that
$$\int$$ cf= c $$\int$$ f
(both integrals goes from a to b i didn't kno how to put it in the integral)

I'm not sure how to go about this problem
Please help me out~
Thanks

 

[HallsofIvy]

When you are completely "stuck", look back to the definitions.

How have you defined $\int_a^b f(x) dx$?

 

[tomboi03]

okay, i just got a hint saying that it would be best if we treat this separately with the cases c$$\leq$$0 and c$$\geq$$0.

how would that help me out? wouldn't it just be the same thing except it will be either negative or positive?

 

[HallsofIvy]

How have you defined $\int_a^b f(x)dx$?