Given the following function $f,$ define $f(1)$ so that $f$ is continuous at $x=1,$ if possible:

$f(x)=\frac{x^2-2x+1}{x^2-6x+5}$

Given the following function $f,$ define $f(1)$ so that $f$ is continuous at $x=1,$ if possible:

$f(x)=\{\begin{array}{ccc}3x-1,& if& x<mn>1</mn>\\ x^2+1,& if& x>1\end{array}$