As the sun ages, what will happen to life here on earth? why?

Our Sun will slowly get hotter as more and more Helium accumulates in the Sun's core. In ~1 billion years, liquid water will no longer be possible on Earth's surface, and the oceans will completely boil away, resulting in a Venus-like planet. Only thermophyllic bacteria may be able to survive, perhaps at the poles. In ~4-5billion years, our Sun will have converted ~10% of its Hydrogen to Helium, and thus become so hot that Helium to Carbon fusion will begin in earnest, causing the "Helium flash" which will convert our Sun into a red giant, and swallow and vaporize all of the rocky inner planets. It may even blow off a planetary nebula. (Contrary to what the others have said, our Sun will not 'run out' of Hydrogen.) 

See diagram.we use washers to get the area and we will be integrating with respect to xouter radius is the  distance between y = e^x and y = -1    inner radius of washer is the distance between y = 1 and y = -1    the area of one cross-section of a washer is    solid lies between x = 0 and x = 2. the volume is    if you need this expanded, then    the question doesn't say to evaluate, so we're done.   

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