How do you correctly punctuate this sentence?

Literacy instruction should be integrated into each subject, such as math, English, science and history.

Does that help?

If you want to leave the sentence the way your structured it, then remove the comma after "such as." All the rest are correct, with one caveat: the comma after "science" and before "and" is optional.

However, the sentence is vague. Are math, English, science and history the only core subjects, or are they merely examples the many core subjects?

If they're examples, then to make that fact absolutely clear, you should say "including" rather than "such as." But if they are the only core subjects, then the sentence is better written thusly:

Literacy instruction should be integrated into each core subject: math, English, science and history.

Literacy instruction should be integrated into each core subject such as math, English, science and history.