Express $\lim _ { n \rightarrow \infty } \left\{ \sum _ { i = 1 } ^ { n } \left[ \cos \left( \frac { \pi i } { n } \right) \right] \frac { \pi } { n } \right\}$ as a definite integral, then find the limit.

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The Answer of Express $\lim _ { n \rightarrow \infty } \left\{ \sum _ { i = 1 } ^ { n } \left[ \cos \left( \frac { \pi i } { n } \right) \right] \frac { \pi } { n } \right\}$ as a definite integral, then find the limit.

Express As a Definite Integral, Then Find the Limit