Actually, there are several possible end of the universe scenarios being debated, but the earth being swallowed up by the sun's red giant phase is pretty consistent among them.
http://theconversation.com/the-fate-of-the-universe-heat-death-big-rip-or-cosmic-consciousness-46157
This is why I used the qualifier "if not captured by another stellar object or destroyed in the red giant phase"
I seriously doubt that anyone will be around to find out for sure.
Oh, we will be. Of that you can be sure
I would pay $30 to know what sexy looks like in 100 million years. 
Sorry. In 100 million years, for the progressives anyway, there is no sex. For anyone. The biological portion of us (which currently make up 100% of us) will be long cast aside in favour of technology. Biology is too high maintenance and too fragile for space faring. The people who have colonised other worlds before the full adaptation to technology based living no longer look human. For example growing up on Mars with 38% of the gravity of that on Earth, the adaption over thousands of years is what you would consider hideous disfigurements. It's even worse for those that live on Titan. Over time, between the people of Earth, Mars and Titan are literally aliens to each other. Earth is no longer hospitable to life as we like it in 100 million years. Climate change has all but wiped out all life in the oceans starting with plankton, which caused a mass extinction event which cascaded to devastating effects to life on the land. The atmosphere as we enjoy it with the abundance of oxygen has also degraded.
The Earth does suffer a cataclysmic asteroid collision in a little over 100 million years. In Trumps final year of his Presidency, to satisfy his ego he spends billions of dollars on an operation to 'paint' an asteroid. In huge white letters across its 15km diameter are the words 'TRUMP - MAGA'. (so every star gazer far into the future can see his name). Due to the white paint it affects the rotation of the asteroid and thus, ever so slowly is trajectory. Had it not been painted, it would have missed the Earth. The irony is that although it says MAGA, it actually lands on the North American continent. Whoops.
in 4 billion years our descendants (not that they will look much like it) will be enjoying menial existences on the moons of Saturn, Uranus, Neptune and even on Pluto. Our sun will be bright and large enough to make the weather there quite balmy. While Pluto is not considered a planet, it is also ironic it will (in this solar system) be the last bastion of humanity in the solar system. After the sun shrinks to a white dwarf, Pluto ends up 'going rogue' and drifts aimlessly throughout the universe. The core of Pluto remains warm for a long time and we live underground. Those that lived on the moons of other planets don't last very long after the sun 'dies'
It is several billion years later after the merger with Andromeda is complete that Pluto is captured by a new star and is nestled more or less in the outer edges of its 'goldilocks' zone. Aliens from its system find traces of our existence and thus the seeds of our evolution once again revive.
Biological life and the passage of time is so arduous though.