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Question: integral of Dirac

Question:integral of Dirac

banksj3RPI 5 Maple
integration dirac
January 27 2024
1

Performing

II := int( Dirac(x^2+y^2-1), x = -infinity..infinity )

gives 

II = 1/sqrt(abs(y^2 - 1))

with no restriction on y. It seems that the answer (at least to the question I thought I was asking) is actually 

II = 1/sqrt(1-y^2) for y\in[-1,1], 0 else

Am I misunderstaning the meaning of Dirac and its integral?
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