Formulate an Algebraic Expression: Given a=1, b=-1, c=1

To solve this problem, let's form the algebraic expression using the standard quadratic formula:

$y = ax^2 + bx + c$

Given are the values:
$a = 1$,
$b = -1$,
$c = 1$.

Substituting these values into the formula, we have:
$y = 1 \cdot x^2 + (-1) \cdot x + 1$

This simplifies to:
$y = x^2 - x + 1$

Thus, the algebraic expression is $\boldsymbol{x^2 - x + 1}$.

The correct choice from the given options is:

Choice 3: $x^2-x+1$