Asked for the indefinite integral

⌠ln(x+f)
⎮─────── dx
⌡  x+a

Wolfram|Alpha returns

          ⎛  f+x⎞              ⎛a+x⎞
I(x) ≡ Li₂⎜- ───⎟ + log(f+x)log⎜───⎟ + const.
          ⎝  a-f⎠              ⎝a-f⎠

For a = 1.2 - 3.4*i and f = 5.6 - 7.8*i, computing the definite integral between x=2.1 and x=2.3 using this expression yields I(2.3) - I(2.1) = -4.8411 - 11.4393 i, as shown here. But, if instead Wolfram|Alpha is queried directly for the definite integral between x=2.1 and x=2.3, it returns 0.0937041 + 0.0475201 i, as shown here. What is going on?

The two methods of evaluation seem to agree for other integration bounds. E.g., for the integral between x=2.3 and x=2.5, both query types yield 0.0922966 + 0.0442528 i, as shown here and here.

Does anyone know what's happening for the integral between x=2.1 and x=2.3? I'm surprised that Wolfram|Alpha doesn't provide a robust answer as the integral in question arises in the fairly prosaic context of evaluating

          Re(f)
⌠     1  ⌠              1
⎮ dx ─── ⎮      dy ───────────
⌡    x+a ⌡         x+y+i*Im(f)