This paper proposes an iterative soft-decision decoding algorithm for Reed-Solomon (RS) codes. The proposed decoding algorithm combines the concepts of adapting the parity-check matrix and informed dynamic scheduling decoding. The parity-check matrix is re-arranged before each iteration, where the systematic part is mapped to the least reliable bits, consequently reducing their influence on the other bits. Using dynamic scheduling, the more important decoding messages are updated to these least reliable bits, meaning that the majority of the error bits with low reliability can be corrected. When the proposed integrated decoding is applied to (255, 239) RS code, the difference between its frame error rate performance (FER) and the maximum-likelihood (ML) bound can be reduced to 0.8 dB, and a gain of about 0.1 dB is achieved compared to all the previously recorded soft-decision decoding for RS codes.