The numerator will be defined for all x

If the discriminant of x^2 - x + c is < 0, there will be no real x's that make the denominator 0

So...we have that

1 - 4c < 0

1 < 4c

1/4 < c

So....c > 1/4 and the smallest positive integer where c > 1/4 is when c =1