If the underlined phrase is <em>born in New York in 1856, </em>then that would be a participial phrase, which often functions as an adjective in a sentence, like is the case here. Gerund is always used as a noun, and infinitive has the form <em>to + verb </em>(to go, to be...)
The answer is B, you never give personal information and expository is an explaining essay so there is no need to persuade because there is no argument occurring
