[CentOS] centos 6.3, cron and mail script output

Fri Nov 23 07:52:50 UTC 2012
Mihamina Rakotomandimby <mihamina at rktmb.org>

Hi all

I have a '/etc/cron.daily/push-to-backup' script which the content is:

   /usr/bin/rsync [... long options line ...]
   echo "finished pushing to the backup"

Launched manually, it's OK.

Waiting for cron to execute it,
In the "/var/log/cron", I see the starting time and the finish time, and 
I see it take about 10 minutes to make the job. That's very fine, it's 
the expected executioon time

The problem is: I get no EMail.
In "/etc/cron.daily/", I also have "logwatch", whose EMail comes to me 
without problem.
"/etc/aliases" is already setup to forward root and cron emails to my 
email adress.
Testing the MTA (Exim) on command-line: success (anyway, logwatch also 
success on sending email)

On another centos5 machine, the same script, the mail is sent.

On the Centos 6:
   $ rpm -aq | grep cron

On the Centos 5:
   $ rpm -aq | grep cron

How to setup the Centos6 system so that the cron sends me an email the 
script output??