Hi. Apologies for the delay.
In the DayPilot Lite demo, there is one page that demonstrates how to use it with UpdatePanel from ASP.NET AJAX Extensions. That page is UpdatePanel.aspx. You don't need that page unless you want to see how to use DayPilot with UpdatePanel. You can safely delete it.
If you are interested in UpdatePanel integration, it's necessary to install ASP.NET AJAX Extensions 1.0 (note the version number, it's the original release) and rename Web.Ajax.Config to Web.Config. Web.Ajax.Config contains a reference to System.Web.Extensions library which is required for UpdatePanel (and it also contains a ScriptManager).
.NET Framework 3.5 and later include the ASP.NET AJAX Extensions. If you want to use this version you need to update the version number in UpdatePanel.aspx and Web.Ajax.Config (renamed to Web.Config) from "1.0.61025.0" to "3.5.0.0".