I am on the shared host Bounceweb and I am trying to add some rewrite rules to make my links look prettier.
One of these rules is to make the url: http://mysit
\xef\xbb\xbf are three invisible junk characters (at least from Apache's perspective) called the Unicode BOM, or byte order mark. Apache thinks that those characters are part of the command that follows right after. This is what you see in the log, though the characters are escaped so they're visible to the naked eye. \xef\xbb\xbfRewriteEngine
In your editor, especially if your editor is Notepad, make sure you're saving your file without a BOM. This should be selectable in the save as dialog or elsewhere.