The idiomatic expression "an integral part of something" means that it is an essential and indispensable element, without which the whole would be incomplete. Full definition
Clients recognize and appreciate being treated with respect, and being acknowledged as integral parts of a team whose shared purpose is to attain a most favorable outcome for them and their children. (nollettilawgroup.com)
Ramsey, Ox, Gibbs and Szczesny are better than average (not world class yet) and will be and integral part of our team for the next 7 - 8 years. (justarsenal.com)
His partnership with Lionel Messi was the stuff of dreams, and with Xavi out of the line - up, it was Alves who served as the safe option and arguably the most integral part of the team as the link between defense and attack. (barcablaugranes.com)