Answer
$\int_{0}^{\pi/4} tan(x) dx$.
Work Step by Step
By using the definition of the definite integral, P is a partition of $[0,\pi/4]$, therefore the lower and upper limits of the integration are 0 and $\pi/4$. $f(c_{k})=tan ({c_{k}})$ is the function in the additive of the Riemann sums, therefore $f(x)=tan(x)$. Therefore the solution is: $\int_{0}^{\pi/4} tan(x) dx$.
