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I want to calculate $$\int_{-1}^i \zeta(z) \, dz $$ Using Wolframalpha gives me approx. $0.36$ while using Mathematica gives me approx. $0.07 - 0.28i$. Which of these is correct and why is there a difference?

Michael Hardy
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Tom Bombadil
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    WolframAlpha also gives the second answer if you click "more digits". I'm guessing this is a bug with complex-valued integrals, it seems to be returning the sum of the absolute values of the real and imaginary parts. – Andrew Dudzik Aug 24 '21 at 23:16
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    Is this a path-dependent integral in the complex plane? – David G. Stork Aug 25 '21 at 00:46
  • I thought that Zeta is holomorphic and therefore the integral is path-independant. But I might be wrong? – Tom Bombadil Aug 25 '21 at 22:00

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