The answer is A: I stayed up all night doing homework; however, I just couldn't concentrate.
Semicolons are used, most commonly, to connect two independent clauses without using a conjunction; however, if a conjunctive adverb is used in the sentence (the most common conjunctive adverbs include however, otherwise, therefore, then, finally, likewise, consequently, nevertheless, moreover, and however) the semicolon helps the conjunctive adverb join the two independent clauses, like in the answer above.