It's possible that you reached this article purely by chance, or you may have Googled 'how to change the default search engine in Microsoft Edge'. However you got here, the fact that you're reading this indicates that you're either interested in Windows 10's Edge, or actively use it -- and this means there's something you need to know.
If you fall into the latter camp and use Edge's InPrivate mode to cover your online tracks, you might want to think about changing your web browser. Edge has already got some stick for its lack of extension support -- "it's coming, it's coming!" Yeah, whatever... so's Christmas -- but now it turns out that InPrivate mode is a privacy nightmare. It is possible to peak behind the curtain and see which sites have been visited when using a browsing mode that should mask this.
There are similar features found in other browser. Chrome has Incognito mode, Safari has Private Browsing, Firefox has... actually, Firefox has Private Browsing too. Whatever the name, what these browsing modes all have in common is that once the browser is closed, there is no record of which sites have been visited. That's not to say that ISPs and law enforcement agencies wouldn’t be able to determine the browsing history, but from a local point of view it is as though no browsing has taken place.