1. The problem statement, all variables and given/known data Prove if f is integrable on [a,b] then [tex]\exists c[/tex] [tex] a\leq c \leq b[/tex] so that [tex]\int_a^cf = \int_c^bf[/tex] 3. The attempt at a solution I know that you have to use the first fundamental theorem of calculus and start with: [tex]g(x) = \int_a^xf(t)dt-\int_x^bf(t)dt[/tex] I'm not sure how to get started and to use this fact to help prove it. Any help would be really appreciated. Thanks!