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Something wrong with this integral (see text)

Hi All

I calculated two expressions:

FullSimplify[Integrate[(-L^2)/(L^2 + 1)*Cos[L], {L,0, Infinity}]]


FullSimplify[Integrate[(-1)/(L^2 + 1)*Cos[L], {L,0, Infinity}]]

They gave the same result, but in the first expression when we take
L->Infinity, it's impossible to take integral, but MAthematica CAN do that.

What the explanation of this?

Tnx for any help.


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