Answer
$f(x)=\displaystyle \frac{x^{2}}{2}+1$
Work Step by Step
The slope of f(x) at x=a is $f^{\prime}(a)$
Given $f^{\prime}(x)=x$ (the slope at x),
$f(x)=\displaystyle \int xdx=\frac{x^{2}}{2}+C$
Given f(0)=1, we find the particular C:
$f(0)=\displaystyle \frac{0^{2}}{2}+C=1$
$C=1$
So,
$f(x)=\displaystyle \frac{x^{2}}{2}+1$
