deleted calculator - how do I get it back?

My daughter managed to delete the calculator which is preinstalled on the IPhone (i.e. I didn't buy it as an appplication) from my phone. How can I get it back?
She also managed to delete one of the purchased applications - this should have been backed up during synchronising but hasn't been automatically put back on with recent syncronisations. Is there a way of telling the back up to put it back onto the phone?

Thanks!