Incorrect spelling


Incorrect spelling, explanation: build-in is an incorrect form because to have an adjective meaning we need a verb in past participle form. Therefore built-in is the correct form, as built is the past participle of build. The only correct option here is built-in as it has an adjective role.

Correct spelling


Correct spelling, explanation: this form is the correct one because built-in is an adjective. Therefore past participle must be used: when a past participle comes with no auxiliary verb, it usually has an adjective role. Built is the past participle of build, thus built-in is the correct form, not build-in.

Definition of built-in:
adjective, creating an integral part with something
Tom and Rose have a built-in swimming pool next to their house.
This cupboard is built-in, I think it really fits there.