Override 'From' address with SingleEmailMessage

You can use the setOrgWideEmailAddressId(ID) instance method of SingleEmailMessage. To do this, first you have to setup your org wide default email address by going to Setup | Email | Organization-Wide Addresses. You can then get the ID of that email address and use that in the instance method.

OrgWideEmailAddress[] owea = [select Id from OrgWideEmailAddress where Address = 'example@example.com'];
Messaging.SingleEmailMessage mail = new Messaging.SingleEmailMessage();
if ( owea.size() > 0 ) {
    mail.setOrgWideEmailAddressId(owea.get(0).Id);
}