I looked through it and couldn't find anything. Is there something i am missing?
Both of these integrals depend on the path you are taking from 0 to 1 + i. For example going from 0 to 1, then from 1 to 1 + i gives (3/2) + (1/2)i. Going along the straight line from 0 to 1 + i gives (1/2)i.