Line integral across a vector field

[clandarkfire]

I've attached the problem as a picture.

Generally, this would be a simple problem if I were to apply Green's theorem. But I can't use Green because D would not be a simply connected closed region; the vector field isn't defined at the origin.
Could someone please give me an idea of where to start?

 

[Dustinsfl]

I've attached the problem as a picture.
View attachment 52525
Generally, this would be a simple problem if I were to apply Green's theorem. But I can't use Green because D would not be a simply connected closed region; the vector field isn't defined at the origin.
Could someone please give me an idea of where to start?

Break it up into two integrals and evaluate each path separately and then add them together.