What is the smallest integer value of $c$ such that the function $f(x)=\frac{x^2+1}{x^2-x+c}$ has a domain of all real numbers?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the smallest integer value of $c$ such that the function $f(x)=\frac{x^2+1}{x^2-x+c}$ has a domain of all real numbers?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1
What is the smallest integer value of $c$ such that the function $f(x)=\frac{x^2+1}{x^2-x+c}$ has a domain of all real numbers?
train