How can I search the Google Calendar from the Android phone? I would have thought that Calendars would be searchable, but opening up the Calendar, and clicking on the search button searches websites via Google web search, but does not search my Calendar.

This is on a Motorola Photon 4G Android version 2.3.4 (not rooted).

How do I do it on the phone (it is possible from a desktop browser).

I have installed the Google Search app, and tried to add Calendar to the list of applications it would search, but there is no entry for Calendar.
On Ice Cream Sandwich, the search button is in the "..." menu: