Using a trapizodial rule (what you implied) is not the best method to use.
First, you need to seperate the continious weights (shell, deck, longitudinals) from the descrete weights (frames, pipes, tankage, pumps,etc).
The continious weights are calculated using Simpsons 1st and 2nd area rules for a single unit of length around some station (usualy Sta. 0, the FP). The descrete weights and thier moments are just summed. The total of the moments is divided by the total of the weights to get the LCG.
the LCB is determined the same way as the continious weights, but using station area as the ordinate.
Normally, Displacement does not equal Weight and LCB does not equal LCG. To correct both of these, ballast is added so that weight= displacement and LCG= LCB. If you are really far out, you may end up with negative ballast (which will require the removal of weight or an increase in draft) or a ballast position that is outside the hull (again weight will need to be shifted or the hull lines adjusted). Normally, it takes several turns through the design spiral before weight, displacement, LCG, and LCB close to a buildable solution.
See this quick overview slide show preliminaly hull design and hyrdostatics concentrating on slides 40-61. http://www.docstoc.com/docs/16813343...M-AND-GEOMETRY