Integral means forming an essential part of the whole. An integral part, integral to the plan, integral design.
It takes to, and the point is that the thing cannot be removed without changing what is left. In mathematics an integral is a quite different thing: the area under a curve, and the word is stressed on the first syllable there.
1adjectiveintegralForming an essential part of the whole.
“Music is an integral part of the school day at this academy.”
integral is a quality.
Latin integralis comes from integer, whole or untouched — in, not, plus tangere, to touch.
Latin
integer — entire
Medieval Latin
integrālis
Middle French
integral
English, today
integral
Middle French integral, from Medieval Latin integrālis, from Latin integer (“entire”); see integer.
Etymology from Wiktionary, CC BY-SA