Actually, from the abstract this looks like a moderately interesting paper. Also note that the slashdot summary is (as often the case) wrong. You can't solve the problem the paper is referring to with integral calculus.

The curve that the paper is talking about is an experimental result, not a formula. All you have are the experimental samples from the curve. Without a formula, you CAN'T do integration, and must rely on a numerical technique. What he's 'invented' here is the trapezoidal rule. He'd do even better with something like Simpson's rule, but that might be impossible to apply if the sample points are not evenly spaced. Similar problems occur for the various Runge-Kutta methods.

Although the numerical technique that claims to be invented here is indeed a basic numerical technique, the paper is interesting for pointing out that the even cruder numerical techniques that have been used before are overestimating the curve area, and that is an interesting result.