Most people realise that all software contains bugs – and even Mathematica contains a few. For example, at version 5.0 the following double integral evaluated incorectly to zero:
This was indeed a bug at version 5.0 – happily cleared at version 5.1.
Some people react to a discovery of this sort by asking how they can ever trust Mathematica again! However, this is very simplistic. Mathematica will make far fewer mistakes that almost any human mathematician. Furthermore, even if Mathematica were a perfect piece of software, you could still make mistakes because of 'bugs' in your input. For example, consider this:
I am sure Wolfram support have received assorted variants of that 'bug' from time to time, but if you look carefully, there is no space between the 'x' and 'y' variables – thereby creating a new variable 'xy' – so this is simply the indefinite integral of a constant.
Thus, you must proceed cautiously before doing something irreversible (such as publishing a paper!) using a result. This is obviously doubly true if a result looks surprising. Do exactly what you might do in a hand calculation – check the result in a totally independent way. The above double integral could have been evaluated in two stages using 1-D integration, or it could have been evaluated numerically using NIntegrate for randomly chosen values of the other constants. Either experiment would have revealed the error.
Mathematica bugs (at least in the kernel) are pretty rare, but so are hard disk failures, but that is hardly a reason not to take a back-up disk copy!