integral( 1/sqrt(x),x, 0,1) = 2sqrt(x)
You cannot use the Riemann integral over here. The function $\displaystyle \frac{1}{\sqrt{x}}$ is even defined on $\displaystyle [0,1]$. If you had $\displaystyle [1,2]$ then it is possible to do it by definition, but not the way you posted the problem.