Hubbard Stratonovich transformation

[aaaa202]

Introducing the Hubbard Stratonovich transformation my book uses an expression for completeness that I don't understand (the one indicated on the picture). Can anyone explain why this is indeed unity?

 

[fzero]

The normalization constant that they refer to being absorbed into the definition of the functional measure is presumably the appropriate power of $\det V$ and other factors that makes that unity. Overall rescalings of the functional measure should drop out of calculations of observables.