How to solve this question
$$ I=\int_{-\infty}^{\infty} \frac{e^{-\iota z t}}{1+z^2} dz $$
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Use $z=x+iy$, use then substitution, or $z=e^{i\phi}$ and use substitution also – Luthier415Hz Apr 28 '22 at 09:34
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For $R > 0$, integrate around a semicircular contour of radius $R$ using the residue theorem. Take $R \to \infty$. – Mason Apr 29 '22 at 16:29