Why are compulsory law associations called an "integrated" bar?

Mandatory bar organizations are called “integrated” because they combine membership with a regulatory function, that is, they have the power to set standards and discipline members. This is a state rather than a federal function, both in admitting lawyers to the bar and disciplining violations, possibly resulting in denial of the privilege of practicing law in the state.

Lawyers are also, of course, subject to the criminal laws of the state.

Some states require membership in a regulatory agency often called the state's bar association in order to permit them to practice law in that state. Such an organization is called a mandatory, integrated, or unified bar.[4][5] and is a type of government-granted monopoly.

https://en.m.wikipedia.org/wiki/Bar_association

The following article also discusses the “integrated bar”: https://ir.lawnet.fordham.edu/cgi/viewcontent.cgi?article=1722&context=flr