built-in vs integral

built-in is not a noun while integral is a noun.

Word	Noun	Adjective	Verb	Adverb
built-in	No	Yes	No	No
integral	Yes	Yes	No	No

As adjectives, built-in and integral are synonyms defined as:

built-in and integral: existing as an essential constituent or characteristic

Other synonyms of built-in include constitutional, inbuilt, inherent.

built-in (noun)	integral (noun)
	the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)

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