does microsoft RMS integrate with .php shopping carts such as MAGE

RMS does not really integrate directly with most shopping cart software. There are some companies, such as Nitrosell, that have developed shopping carts that specifically integrate with RMS, otherwise its all about commutation from the shopping card to RMS. What you need is a software that will create a bridge between the website/shopping card and RMS. We offer such a program called RMS Web Portal. Retail Realms & New West Technologies have similar offerings.