I work for a small telematics company and we received a request from one of our clients about integrating their vehicle GPS locations to their ArcGIS system.  

Our current system simply displays this location data on google maps through javascript.  
I'm not really familiar with GIS, but I began doing some digging. From the best I could grasp, I need to write a web service that their GIS server can access in order to add it to the maps.  

Our system uses a mysql database that holds the data sent to it by the GPS devices. If a GIS map could derive the information straight from the database, that would be fine. The only real thing at that point would be how to define where the GIS server would look for the information. The data stored in the database is very expansive and contains a lot of information that is not pertinent to the map location. So If this is a route that can be taken, what's the best way to go about connecting a GIS server to retrieve information from our mysql database?