Need a nominalized synonym for the word "include"

Three nominalized synonyms or noun synonyms that sprung to mind:

addition • addendum • extra

The above examples, however, only work for the second definition of include in your quote, which means to take into account.

For the first sense of the word (to incorporate, comprise), you could try the following:

component • constituent • element • member • unit • item • ingredient • part • activity • type, etc.

"Include" is a verb. Its corresponding/derived noun is "inclusion". A word with similar meaning is "incorporation" [ =To unite (one thing) with something else already in existence ] (but it's not a synonym).