TOMS437 is a FORTRAN77 library which implements ACM TOMS algorithm 437, which carries out a product type Simpson's integration to estimate the integral from A to B of F(X) * G(X).
While the text of many ACM TOMS algorithms is available online through ACM: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html, most of the early algorithms are not available. This is one of them. I typed it in.
TOMS437 is available in a FORTRAN77 version.
INTLIB, is a FORTRAN77 library which estimates integrals.
QUADRULE, a FORTRAN90 library which can define various quadrature rules to estimate integrals.
TEST_INT, a FORTRAN90 library which cdefines a number of scalar functions of to test routines that estimate integrals.
TOMS436, a FORTRAN77 library which carries out product type trapezoidal integration.
TOMS438, a FORTRAN77 library which carries out product type two-point Gauss-Legendre-Simpson's integration.
TOMS439, a FORTRAN77 library which carries out product type three-point Gauss-Legendre-Simpson's integration.
You can go up one level to the FORTRAN77 source codes.