In terms of the end points, we can also write the formula as

This formula is called the Simpson’s 1/3 rule.

We can also evaluate the integral,

then we get,

 

Let [(x – x₀)/h] = s. The limits of integration become

for x = x₀, s = 0, and for x = x₂, s = 2.

We have dx = h ds. Hence,