Proving the Limit of Integrable Functions on a Closed Interval

[tomboi03]

Prove: If f is integrable on [a , b] then
lim f =0
x\rightarrowa+

the integral goes from a to x.

How do i go about and prove this? I'm confused.
Please help me out!
Thank You

 

[HallsofIvy]

Do you mean
\lim_{x\rightarrow a^+} \int_a^x f(t)dt= 0

The way you have written it, that the limit of f is 0, makes no sense- that certainly is not necessarily true.

My suggestion here is the same as to your other question: use the definition of integral in terms of Riemann sums.

 

[tomboi03]

I've never learn Riemann sum definition.
What is that?

 

[HallsofIvy]

First, is what I wrote what you mean. And if you have never learned Riemann sums, what definition of \int_a^b f(x)dx are you using?