why do we need the fourth derivative of the function to check the error bound in the simspon's rule? I understand that trapezoidal or midpoint rule's error bound needs the second derivative,
but I just don't get why the fourth derivative in simpson's rule
please help me :)
 A: Simpson's Rule is exact for polynomials of degree 3 or less, so the error term can't depend on any derivative less than the 4th. Put another way: the 3rd derivative of a 3rd degree polynomial is nonzero, so it can't be involved in the error term for Simpson, since the error for 3rd degree polynomials is zero. 
A: Not need. In Sendov and Popov, The Averaged Moduli of Smoothness, Wiley,1988, chapter 3, Numerical integration, gives a "complete" answer for your question.
In the recent paper of I. A. Parvanova and P. E. Parvanov (2005) Exact Constants in Estimations of the Error of the
Quadrature Formulae of Simpson with the Averaged
Moduli of Smoothness www.fmi.uni-sofia.bg/lecturers/ma/pparvan/QF.pdf 
there is a very detailed discussion.
Of course, this is a very special topic, so if you want to have some taste of it, the first section, about one and a half page, is enough. I recommend as a prerequisite to investigate the (usual) moduli of smoothness with relation to Jackson(type) theorems in basic approximation/numerical methods books.
Hopefully I could help you.
This is the first time to reedit my earlier answer, sorry for me if I made something wrong.
A: Simpson's rule is identical with  Taylor expansion up to order 4 i.e. O(h^4) that is the term includes the fourth derivative.
