It IS correct, but it's old-fashioned.
It follows the now rather outdated rule that the standard - that is, not emphasised - first-person version of 'will/would' is 'shall/should'. Nowadays, very few people observe this convention except in formal, written contexts. Most people under the age of 40 or so are unaware of this rule.
The example in your book is a relic of former times. You are unlikely to hear this construction, and you will never need to use it.
"I should ignore it, if I were you." :)