I was never so much for the coding part, but rather the fact that he mentions that you can't be sure that the computer adds correctly, and therefore, in essence, the programmer has to convince himself that the output is expected.Salem's answer involves integer ranges, and I think that's too complex. Besides, it doesn't answer the question.
Even with an operation as trivial as addition, the computer is no replacement for the human brain. Only the programmer can know what is right and what is wrong.