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Cauchy's integral formula and residue theorem

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(See attached file for full problem description and embedded formulae)

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Why can (1) be regarded as a special case of (2)?

(1) Cauchy's Integral formula (no need to prove):
is a simple closed positively oriented contour.
If is analytic in some simply connected domain D containing
and if is any point inside , then

(2) Cauchy's Residue Theorem (no need to prove):

is a simple closed positively oriented contour
and is analytic inside and on except at the points
inside , then

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(See attached file for full problem description and embedded formulae)

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This shows a proof regarding Cauchy's Integral formula and Residue Theorem.

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