I am trying to display HTML page in a pageviewer web part. However, when the page is loaded I get a prompt asking me to save the html page. How can I prevent this so that html page is displayed in the pageviewer web part without prompting end user to save first.

This is certainly a Browser File Handling issue. In Central Administration, manage the web application in question. In General Settings, change the "Browser File Handling" option from Strict to Permissive. When browser file handling is set to strict, SharePoint will push out the "X-Download-Options: noopen" header in the http response for certain file types. You can read about this new IE8 security feature that utilizes the noopen header that forces save at http://blogs.msdn.com/b/ie/archive/2008/07/02/ie8-security-part-v-comprehensive-protection.aspx?PageIndex=4.

I ran into the same issue before.  What Diffident mentioned should resolve this issue for you.

Where do we find the "Central Administration" in Office365 sharepoint ? we are using Sharepoint on office365 cloud.

You will not get Central Admin in Office 365 online. Just try renaming the page to .aspx if that will help you.