The lower limit of integration is zero since the LTI system has been assumed to be physically realizable (causal), that is to say, it responds only to past inputs. The assumption of causality, in fact, implies that:
The lower limit of integration is zero since the LTI system has been assumed to be physically realizable (causal), that is to say, it responds only to past inputs. The assumption of causality, in fact, implies that: