### Fundamental Theorem of Calculus and Uniform Convergence

Suppose f is Reimann integrable on [a,b] and let F(x)= ∫_a^x▒f(t)dt for all x ∈[a,b]. Prove that F is continuous on [a,b] (hint: f must be bounded) Let F(x) = {█(x^2 sin(1/x) if 0<|x|≤1,@0 if x=0)┤ and let f(x) = F'(x) Prove that F'(x) exists for all x ∈[-1,1] Find f(x) for all x ∈[-1,1], and prove t