find all values of a and b for which the function will be continuous 
I have to find all values of a and b for which the function will be continuous.
what I do is next: f(0)=1 ; limit of ax+b = b => b=1 ;
and I get stuck with a, can a be anything? 

Yes, you're right!
You only have to have $a0+b=1-0-0^2$, because $f$ obviously is continuous on $(-\infty,0)$ and on $(0,+\infty)$ as it is a polynomial.
So $a$ may be any real number, $b$ has to be equal $1$.
