Error in Mathematica Integration with PrincipalValue-> True

Question

It seems that Mathematica's processing of principal integrals fails in some corner cases. Consider these two expressions (which should give the same result):

Integrate[UnitBox[x]/(x0 - x), {x, -Infinity, Infinity},
  PrincipalValue -> True, Assumptions -> {x0 > 0}] /. x0 -> 1 // Simplify
Integrate[UnitBox[x]/(x0 - x) /. x0 -> 1, {x, -Infinity, Infinity}, 
  PrincipalValue -> True]

In Mathematica 7.0.0 I get

I Pi+Log[3]
Log[3]

Was this fixed in later versions? Does anyone have any ideas for a (more or less) common workaround?

EDIT: the two above expressions should calculate the same result, first calculating the general form of the integral and evaluating it with x0=1, and the second, performing the integral with x0set to 1. Since the exact meaning of Cauchy has a precise mathematical definition, Mathematica must give the same result or refuse to answer.

2: , , -1 Integral ( , -, ):

-Integrate[ UnitBox[x]/(x0 - x), {x, -Infinity, Infinity}, PrincipalValue -> True, Assumptions -> {x0 > 0}]
 Integrate[-UnitBox[x]/(x0 - x), {x, -Infinity, Infinity}, PrincipalValue -> True, Assumptions -> {x0 > 0}]

Answer 1

, PrincipalValue. PrincipalValue "", , Integrate.

EDIT: Mathematica, , . , Trace[]. ( ), , x0 PrincipalValue.

EDIT2: . , , x = 1/2 x0 , .

Answer 2

, 8.0:

In[1]:= $Version
Out[1]= "8.0 for Mac OS X x86 (32-bit) (November 13, 2010)"

In[2]:= 
Integrate[UnitBox[x]/(x0 - x), {x, -Infinity, Infinity}, 
   PrincipalValue -> True, Assumptions -> {x0 > 0}] /. 
  x0 -> 1 // Simplify

Out[2]= Log[3]

In[3]:= Integrate[
 UnitBox[x]/(x0 - x) /. x0 -> 1, {x, -Infinity, Infinity}, 
 PrincipalValue -> True]

Out[3]= Log[3]

Answer 3

Well Wolfram Alpha, , Mathematica, : (3) +

http://www.wolframalpha.com/input/?i=Integrate[UnitBox[x]%2F%28x0+-+x%29+%2F.+x0+-%3E+1%2C+ {x% 2C + -Infinity% 2C + Infinity}% 2++++ PrincipalValue + -% 3E + True]

, , , ? , . , , , . Integrate, , Integrate .