A way to remember the formula for Simpson's rule for calculating the approximate area under the curve is given by:
h/3 [ y0 + 4 ( y1 + y3 + y5 + ... ) + 2 ( y2 + y4 + y6 + ... ) + yn ]
where h is the common width between intervals, I don't bother remembering the b - a.
The pattern is FOTE, Four Odd Two Even for the function values.