[olooney]

Is this not just the trapezoidal rule for numeric integration?

https://en.wikipedia.org/wiki/Trapezoidal_rule

It's not even a particular good choice for the specific problem (glucose curve) because the trapezoidal rule will systematically underestimate the true area when the curvature is always negative. Simpson's rule is almost always a better choice:

https://en.wikipedia.org/wiki/Simpson%27s_rule

Fun fact: although the method is attributed to the 18th century mathematician Simpson, Kepler is known to have used it in the 17th century.