Let $\displaystyle n$ be a fixed integer $\displaystyle >0;$ consider the function

$\displaystyle f_{n}(x) = \{0, if (x = \frac{1}{n}, \frac{2}{n},...,\frac{n-1}{n}), 1, otherwise.\}$

Prove directly from the definition of integrability that $\displaystyle f_{n}(x)$ is integrable on $\displaystyle [0,1].$

All I've got so far is that: $\displaystyle M_{i} = (\frac{i}{n}); m_{i} = (\frac{i-1}{n}); \Delta x_{i} = \frac{1}{n}.$

Any help? Thanks