# Just Find Its Antiderivative Right?

Evaluate the Riemann integral

$\int_0^1 \frac{1}{ \sqrt{x} } \, dx .$

Note: The Riemann integral of $f$ equals $S$ if the following condition holds:

$\forall \epsilon > 0$, $\exists \delta$ such that for any tagged partition $x_0, \ldots , x_n$ and $t_0, \ldots , t_{n-1}$ whose mesh is less than $\delta$, we have
$\left| \sum_{i=0}^{n-1} f(t_i) ( x_{i+1} - x_i) - S \right| < \epsilon.$

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