The mantra of utilitarianism is to maximize total happiness. Since the quantity they are hoping to maximize is aggregate it does not depend on any specific time frame. Meaning, when the utilitarian is deciding what actions they ought to take, they need to consider not only those who are alive, but also everyone who may yet be born.
Since more people being born leads to more happiness being contributed, the longevity of the human race is paramount to the utilitarian. The scientific community has predicted many global extinction event may loom either in the near or far future for humanity. Managing to overcome or avoid problems such as global warming, nuclear war, or even the death of our own sun would allow the human race to live on for countless more generations, and thus creating more happiness than could possibly be produced by just the population living today.
So I guess the point I’m making is that the utilitarian ought to consider how their decisions will affect the longevity of the human race more critically than how they will affect people’s current level of happiness.
