Lebesgue Inequality: Prove from Definition

[henry22]

Homework Statement

Show from definition that if f is measurable on [a,b], with m<=f(x)<=M for all x then its lebesgue integral, I, satisfies

m(b-a)<=I<=M(b-a)

Homework Equations

The Attempt at a Solution

I know that the definition is that f:[a,b]->R is measurable if for each t in R the set {x in [a,b] :f(x)>c} is measurable.

But I don't see how this helps?

 

[henry22]

Do I need to use a summation somewhere?