$ Let~S,~T\_n~:(C[0,1],~||~||\_∞)→(R,~|~|)~be~a~linear~operator.$

$S :=\int\_{0}^{1}f(x) dx \\$

$T\_n := \frac{1}{n}(\frac{1}{2}f(0) + \sum\_{k=1}^{n-1} f(\frac{n}{k}) + \frac{1}{2}f(1))$

$Show~that~S,~T\_n~are~bounded~operators~and~||S-T\_n||~=~2$

I solved S and T\_n are bounded, but I have no idea how to solve the latter.