Set server-side environment variables in integration testing

My Rails application uses the SERVER_NAME environment variable to
decide how to display some of the web pages.

I want to do integration testing with this application but I do not
see how to force the request object's environment variable SERVER_NAME
to a particular value.

I would like to do something like this in the integration test file

  request.env["SERVER_NAME"] = "www.example.com"

This does not work. Any suggestions?