How does the equation (3.4.3 ) resulted after deforming C into C' ? Can anyone explain this?

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My question might be irrelevant or not according to the standard of this network. But I really appreciated if someone could explain the results in the image below. I really can't understand how the right hand side of the 3.4.3 is solved to a integral below in the image and pi is completely vanished. thanks
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