I vaguely remember seeing in my English book that 'verb-ing' form should come after 'used to', no? Like 'I used to shutting my door' in this case.

Rebecca

Actually, that's incorrect. You cannot use "used to [verb]-ing," but you can use "used to [verb]" or "used to go/do [verb]-ing." For example, you can say "I used to bike" or "I used to go biking," but not "I used to biking." It's okay to use a -ing form verb in the same sentence, but another verb in its base form needs to precede it. Ex: I used to love going to the beach in the summer, but now it's too crowded. Ex: She used to always take this train to work.