Definite integrals, areas and volumes

For $y=x^2$ on $[0,2]$, predict whether left- and right-endpoint rectangle sums lie above or below the integral.

In a spreadsheet or calculator, use n equal strips with width $2/n$ and compare $n=2,4,8$. Keep a column for height times width, then sum it.

Compare both sequences with the exact integral and explain why their separation shrinks.

State which property of this curve justifies the ordering; endpoint choice alone does not give that ordering for every curve.