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.
$y=x^2+\int_{1}^{x} \dfrac{1}{t} dt$
or, $y'=2x^{2-1}+\dfrac{1}{x}=2x+\dfrac{1}{x}$
and $y''=2x^{1-1}+(-1)x^{-1+1}=2-\dfrac{1}{x^2}$
Now, $y(1)=1$ and
$y'(1)=2+\dfrac{1}{1}=3$
