  The main focus of this paper is on determining the highest non-vanishing
local cohomology modules of \Omega_(B/R), \Omega_(B/V)(\Omega_(B/k)) where R is
either a complete regular local ring or a complete local normal domain with
coefficient ring V (field k) and B is its integral closure in an algebraic
extension of Q(R). Similar problem is also studied over a normal domain R
containing a field k of characteristic 0. In this connection new observations
on the direct summand property for integral extensions are also presented.
