Main Question or Discussion Point
In the fundamental theorem of calculus, why does f(x) have to be continuous in [a,b] for [itex] F(x) = \int_a^x f(x) dx [/itex]?
Right. That helped alot. Thanks. :)It's hard to answer a question in which the premises are false! There is NO requirement, in the Fundamental Theorem of Calculus (the part that say "if [itex]F(x)= \int_a^x f(t)dt[/itex] then F'(x)= f(x)") that f be continuous. It might that your text book is proving it with the added assumption that f is continuous because then the proof is easier. But it can then be easily extended to functions that are not continuous.