Question: Integral of Dirichlet with LineInt


I am trying to calculate the Dirichlet integral with the residue theorem and the LineInt command. I use the classic lace (Cf below) and the function exp(iz)/z. I don't understand why the LineInt function returns zero on the top semicircle. The result should depend on r and only be zero for limit(%, R = infinity).

Thanks for your help.

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