OSM on my website

I currently use the API for optimizing routes. Works great.

I would like to incorporate that data on a map on my website. Is there a way to do that?

RouteXL does not have a route embedding option as such.

You can however construct a custom map using other software libraries. E.g. you may take a look at Leaflet, which we also use for our user interface:

http://leafletjs.com/