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Bug in Calculus`DiracDelta`


I know normally "it's the user, stupid!" but this one seems real.

In[1]:=    <<Calculus`DiracDelta`

In[2]:=    Integrate[DiracDelta[Cos[x]],{x,0,\[Pi]}]

Out[2]=  1

That's what I agree with but the next line I cannot:

In[3]:=    Integrate[DiracDelta[Cos[x]],{x,\[Pi],2\[Pi]}]

Out[3]=  0

Any comments/insights/etc. pp.?

Cheers, Martin.



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