Bound

When Changing Auto Insurance Companies, Am I Bound By Law To Show The New Policy To The Old Insurance Company?

Say, today is 1st Feb’09. I had an auto policy (from Farmers) that expired on 1st Jan’09. Today, I buy a new policy from a different insurance company(AAA).
When I discontinue service with Farmers, am I bound to show the new insurance policy to them? Also, will I get charged for the period from 1st Jan’09 to 31st Jan’09 by Farmers?