(More challenging): Find an example of a function f:[0,∞)→R integrable on all intervals such that limn→∞∫0nf converges as a limit of a sequence (so n∈N), but such that ∫0∞f does not exist. Hint: For all n∈N, divide [n,n+1] into two halves. On one half make the function negative, on the other make the function positive.