They have multiple means of monitoring your site. These companies can ping the server, they can even check your shopping cart to see if it works correctly. The way it works is they have servers (monitoring stations) located around the globe. Each server can either check your site at the same time or they usally rotate checking your site every X minutes. If one monitoring station checks your site and can't reach it, the next monitoring station has to confirm the failure before sending you a down alert.
There is nothing to integrate. You just give them the ip or domain and thats it.