Answer
$9$
Work Step by Step
Here, we have $\dfrac{dc}{dx}=\dfrac{1}{2 \sqrt x}$
$\dfrac{dc}{dx}=(1/2)x^{-1/2}$
This implies that
$c=\int_0^{x} \dfrac{1}{2} t dt$
or, $[t^{1/2}]_0^{x}=\sqrt x$
Thus, $c(100)-c(1)=\sqrt {100}-\sqrt 1=10-1=9$