Math Help - integration

1. integration

show that $
\sum\limits_{k = 1}^n {\frac{1}
{{k^s }}} = \frac{1}
{{n^{s - 1} }} + s\int\limits_1^n {\frac{{\left[ x \right]}}
{{x^{s + 1} }}dx}

$

with s not equal to 1