Proof of proficiency in mathematics
Unfortunately, there's no way around crappy grades (other than explaining what happened in your personal statement). But as far as showing that you are competent in these subjects on a grad school application you could:


Do a project which would clearly require knowledge of these topics.
Take the Math Subject GRE and do well, assuming you're applying to programs which care about the subject GREs. The risk here is that what's covered on these exams isn't a perfect match for your integrated courses, but there is a lot of overlap.