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Integrate with PrincipalValue->True


Can someone explain to me how Integrate calculates the following improper integral?

In[42]:= $Version
Integrate[Sqrt[x]/(1 - x^2), {x, 0, a}, 
   PrincipalValue -> True, Assumptions -> 
     a > 1]

Out[42]= "6.0 for Microsoft Windows (32-bit) (June 19, 2007)"

Out[43]= ArcCoth[Sqrt[a]] - ArcTan[Sqrt[a]]

Thanks,
Charles


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