Answer
See below.
Work Step by Step
We know that $\int x^{n} dx=\dfrac{x^{n+1}}{n+1}+C$
where $C$ is a constant of proportionality.
$y=\int_{0}^{x} (1+2 \sqrt {\sec t}) dt$
or, $y'=1+2 \sqrt {\sec x}$
and $y''=2 (1/2) (\sec x)^{-1/2} (\sec x\tan x)=(\sec x)^{-1/2+1} \tan x=\sqrt {\sec x} \tan x$
Now, $y(0)=0$ and
$y'(0)=1+2 \sqrt {\sec 0}=3$
