(You can use standard results in any proofs). Are the following 2 functions Lebesgue integrable over the interval I?

A) I = $\displaystyle [1,\infty)$ with $\displaystyle f(x) = (-1)^n/n$ if $\displaystyle n \leq x < n+1, n = 1,2,3...$

B) I = [0,1] with $\displaystyle f(x) = (-1)^{n(x)}/n(x)$ where n(x) is the largest integer n such that $\displaystyle nx \leq 1$