A New Proof of the Integral Localization Formula for Equivariantly   Closed Differential Forms
  In this article we give a totally new proof of the integral localization formula for equivariantly closed differential forms (Theorem 7.11 in [BGV]). We restate it here as Theorem 2.   This localization formula is very well known, but the author hopes to adapt this proof to obtain a more general result in the future. 
Matvei Libine