There's no reason for you to write this script.
/etc/init.d/mysql is an
init(1) script, so just use that:
# update-rc.d mysql defaults
If that doesn't work, you might need to look into the more advanced
update-rc.d options. For instance, maybe you are using an uncommon runlevel, and the default runlevels for the provided
mysql script don't include that.
If you were actually trying to get something to run on startup which doesn't already provide an init script, you'd need to remove the
sudo bit. init scripts run as root already. You actually have to drop permissions if you need your program to run as another user.