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Bug in LaplaceTransform?

Dear reader,
how can it happen that Mathematica throws out -i for the Laplace 
transform of one,

LaplaceTransform[1, t, I] = -i?

After all the Laplace transformation (with s = I) is defined as

Integrate[Exp[-I t], {t, 0, Infinity}]

and should be undefined. Am I wrong or is this a bug?

Thanks for an answer!

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