It makes perfect sense - and I really appreciate that you took the time to write such an elaborate answer.
However, the teacher has explicitly stated that the problem should be solved without the use of integrals... Hence my fruitless attempts shown earlier.
Since the Simpsons formula is...
Simpsons formula and the volume of a pyramid frustum
Normally I consider myself quite adept in mathematics, but I simply lack the right idea and/or the mathematical creativity to solve this assignmenent:
"Prove that the Simpsons formula V = 1/6 * h * (Ab + 4Am + At) can be used to calculate...