Can you use residues to calculate the integral of the real-valued function sin(x)/x from a to b?

[Random Variable]

I'm only aware of being able to do it for -infinity to +infinity.

 

[KillerCharlie]

From what I remember, you can do integrals that go to or start at 0. You can also do integrals that go from 0 to 2pi - I remember solving a lot of integrals with that.

That's all I remember for sure - but I'm pretty sure there are integrals you can do that don't go to/from infinity or 0 to 2pi.

I took this crap less than a year ago and don't remember anything.

Edit: See example V

 

[CP5670]

In general, you can do some tricks with these problems to make it work, but this particular integral cannot be expressed in terms of elementary functions anyway. You need to introduce new functions to write it out in closed form. These are the obvious candidate.