How to find primitive function?

noamriemer

Hello! I am having trouble understanding the whole primitive function thing in complex analysis.

How do I check if a certain function, say [itex] \frac {sin(z)} {z} [/tex]
has a primitive, say in C/{0} ?
What is the intuition? My intuition is that 0 is the only singularity, so if it is out of the picture, everything should be alright? (I saw that there is no primitive for it- but don't understand how to determine...)
How do I prove there is a primitive? After all, I can't calculate infinite number of integrals over closed laps... Thank you!