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Good point, now that you mention it I do remember that notation from high school books. However I think that is still the non-rigorous way of defining the integral. It may be standard practice for HSC problems, I am not sure. To see more about what I was talking about look at page 3 of...

This is an interesting problem, however I am not sure the answers above rigorously prove it, as an integral is defined to be the limit between the upper and lower Riemann sums, and here we are technically asked to evaluate an infinite sum not an integral. Maybe the best we can do without...

Re: HSC 2014 4U Marathon dunjaaa not sure if what you wrote is correct, it's a bit difficult for me to follow all your steps.