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Integrate is not additive?


The following input returns unevaluated:

Clear[f];
FullSimplify[Integral[f[x], {x, 0, 1}] +
  Integral[f[x], {x, 1, 2}] -
  Integral[f[x], {x, 0, 2}]]

Is there a good reason for it not to return zero?
Perhaps the problem of singularities? Principal values?

Best regards,
Gianluca Gorni


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