The correct options are
A To understand our past and see if we can figure out our future.
C Because we can learn from the mistakes of our ancestors.
We need to study history to understand our past better so that we could learn from the mistakes and figure out our future. This future should also be free of any mistakes which the society had made in the past. Also, interest in a subject varies from person to person. So history might be interesting to some, science to others.