Open your configuration file:

# vi /etc/mail/sendmail.mc

Append or modify macro that read as follows

:define(`SMART_HOST',`mailhost.brm.pri')

If line contains word, dnl remove the dnl word.

Regenerate a new sendmail.cf config file with m4 command:

# m4 /etc/mail/sendmail.mc > /etc/mail/sendmail.cf

Restart sendmail service:

# /etc/init.d/sendmail restart

Edit /etc/sendmail.cf file and locate the the section that begins with DS. Edit as follows:-

DSmailhub.brm.pri

Note no spaces

You will need to restart sendmail to activate the changes made in the sendmail.cf file.
On AIX:-

refresh -s sendmail

On Solaris10:-

bash-3.00# svcadm restart svc:/network/smtp:sendmail