I The first choice is correct; the remark of user Edwin Ashworth makes precise that "significantly" is an adverb of degree (that could be confused with an adverb of manner if one forgets that it confers extent). Although this type of adverb is usually placed before in a mid position (ref.) "significantly" is an exception and can be at the end.
When using these adverbs, be careful not to place them between the object and the verb. They often fit best after the sentence’s object or main verb.
II The second shows a case of split infinitive (ref.). The practice of the split infinitive has come and gone in the English language (ref.) and today it has reappeared, as promoted, I believe, by American English; it has become almost universally correct (ref.: "In colloquial speech the construction came to enjoy widespread use. Today, according to the American Heritage Book of English Usage, 'people split infinitives all the time without giving it a thought'. In corpora of contemporary spoken English, some adverbs such as always and completely appear more often in the split position than the unsplit.").
Notwithstanding this regained overwhelming interest for the split infinitive there are authorities advocating to avoid the practice of placing the adverb betwween the particle "to" and the base form of the verb (many teachers among others and even in the USA) (ref.).
There are a significant number of users of the English language who avoid the split infinitives and here is a discussion on the ways to achieve that: ref.. Note that the placement that is recommended in the reference in "I" does not mention the possibility of splitting the infinitive as being on an equal footing with the placement after the object (which is the case in the first sentence).