HP50 : indefinite integral of '0^x' gives '?' and 0 for '0*x'

[Gil]

Ok for the undefined function '0^x'.

But what about the well defined function '0*x'?

Integral of (0*x) should be simplified before calculating and (logically?) be equal to integral of (0) = constant (as correctly answers Wolfram Alpha for the aforementioned indefinite integral).

Or am I wrong?

On the HP50G, however, '0*X' INTVX (with no bounds) gives zero, as it has been initially calculated with a general formulae a*x²/2, and then the factor a is replaced by its original value a=0, which gives a final value of 0, a special case — indeed a correct result when settling real bounds with the HP50G and executing EVAL command
or —>NUM command.