Integration on a open interval?

[GreenPrint]

Homework Statement

I was wondering how one integrates on a open interval. For example let's say I wanted to integrate the function f(x) = x^2 + 2x + 3 on (2,7). Note that it's on the OPEN INTERVAL not closed of all the x values from 2 to 7 not including 2 to 7. I'm not trying to integrate on [2,7] but on (2,7). How do I do this? Thanks. Any ideas or suggestions or anything at all would be appreciated.

Homework Equations

The Attempt at a Solution

 

[Dick]

It doesn't make any difference. Why do you think it does? The contribution from the endpoints is zero.

 

[GreenPrint]

I know it may not make a difference for this function but what about functions whose anti derivatives are different if you were to take the left hand limit of the anti derivative and the right hand limit of the derivative at the points that were to determine the open interval

 

[Dick]

I know it may not make a difference for this function but what about functions whose anti derivatives are different if you were to take the left hand limit of the anti derivative and the right hand limit of the derivative at the points that were to determine the open interval

The only way the contribution from a single point can make a difference is if you are integrating distributions with singularities. Like delta functions. Distributions are different from functions. Are you integrating distributions?