The Simpson approach states that the "integration range [a,b]" can always be divided into n (n must be even) strips
of width h = (b  a) / n.
Applying the Simpson's rule to two adjacent strips:
^{xi+2}∫_{xi} f(x)dx = h/3 [f(x_{i}) + 4 f(x(_{i+1})
+ f(x_{i+2})]

Then the integral can be obtained by the sum:
I = ∫^{b}_{a} f(x)dx =
∑^{n}_{i=0,2,4,...} ∫^{x i+2}_{xi} f(x)dx =
h/3 ∑ ^{n}_{i=0,2,4,...} [f(x_{i>}) + 4 f(x_{i+1}) + f(x_{i+2})]

It must also be stated that the Simpson's 1/3 rule requires the number of strips n to be even. If this condition is not
satisfied, it is posible to integrate over the first (or last) three strips by using Simpson's 3/8 rule (which is another condition):
I = 3h/8 [f(x_{0}) + 3 f(x_{1}) + 3 f(x_{2}) + f (x_{3})]

and then use the Simpson's 1/3 rule for the rest of strips. Although a bit confusing it is really very simple to implement this rule.
