$ mv config.pl app.pl
$ git status
$ git add app.pl
$ git rm config.pl
($ git add -u)
examples/out/status_14.txt
# On branch master
# Changes to be committed:
#   (use "git reset HEAD <file>..." to unstage)
#
#   renamed:    config.pl -> app.pl
#
$ git commit -m "rename"

$ git mv old.pl new.pl

Try also moving a file and changing its content a bit.