integrality vs integral

integrality and integral both are nouns.

Word	Noun	Adjective	Verb	Adverb
integrality	Yes	No	No	No
integral	Yes	Yes	No	No

integrality (noun)	integral (noun)
the state of being total and complete	the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)

integrality (adjective)	integral (adjective)
	of or denoted by an integer
	existing as an essential constituent or characteristic
	constituting the undiminished entirety; lacking nothing essential especially not damaged