Student or Learner
One of the usages of shall is that it is used in the sense of do you want me/us to do something as in this sentence:
Shall I close the door?
Now, my grammar book says that should is used as the past form of the shall in sentences meaning do you want me/us to do something and it softens the idea as in this sentence:
Should I close the door?
Now, I would like to assure that is this sentence should I close the door? in the past tense the same as simple past or it just softens the idea?
Present — 'It's cold in here. Should/Shall I close the door?'
Past — 'The cat just ran out. Should I have closed the door?'