Migrating website, does all the link paths change automatically? or ...

Hi, Just a general question, as fairly soon i need to move a website from one path to another. Does the links and paths of the domain automatically update or is there a way to batch automate to update these paths when moving a domain up one folder in the ftp?
e.g. http://www.domain.com/testingsite/page1 (current situation) will need to change to http://www.domain.com/page1 (so in this case taking out the "/testingsite" from the path?