But you didn't show that the function is defined for irrational numbers, and you didn't use the standard definition of an integral as a limit of partitions, which I thought was the subject of this thread, so the example is meaningless.
But you win. I am now replying from the local library since after I switched from MHF back to the internet from my last reply to Plato I got a blank screen and now can't get back on. Restarting my modem usually works, but now doesn't. Looks like I'm in for massive inconvenience. Is that your answer to my questions?
Having my computer infected is better than being banned because there is no onus attached to it.
Hope I haven't shut down the local library.