\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Find the value of the definite integral \(\displaystyle \int_0^1 \frac{x}{x^2+1} \,dx\).
\(\displaystyle\int_0^1 \frac{x}{x^2+1}\;dx =\)