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Integrals involving the Heaviside function


I need to perform (many) integrals whose simplest example is
  Integrate[Heaviside[x-2] Exp[-x], {x,0,Infinity}]

where Heaviside is the step function (not available in Mma).
Does anyone have a suitable Mma implementation of the Heaviside
function or suggestion that would allow me to do integrals like
the one above ? 
Manually splitting the interval of integration is not what I want.
I need some automated way (my integrands are defined in terms
of Heaviside[x], actually Heaviside[y^2 -(x^2 -a^2)], where both
x and y are the variables of integration (double integral) and a > 0 ).

Thanks for any help.

  Roque
  oliveria at caen.engin.umich.edu
  Nuclear Eng Dept, The University of Michigan





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