Wiktionary
bound to
phr. (context only with a bare infinitive English) Indicates something which cannot be avoided.
Usage examples of "bound to".
If he ever is seen walking the streets of Calimport again, by the pasha or any of the pasha's many contacts, then I am bound to turn him over for execution.
Therefore, for a long time to come, there are bound to be great masses of people who need to be restrained and controlled and brought along gradually.