Emacs: Convert current buffer to utf-8

I just opened an old TeX file, which was still encoded in latin1. Now I wanted to re-save it as utf-8 in Emacs. This turns out to be very simple, as someone on #emacs at freenode told me. Just hit C-x RET f, and type utf-8 RET. On the next save (C-x C-s), the file will be written as utf-8.