Question 43599
f(x)= -x^3+x^2-x+2.

x     -2  -1  0  1  2
f(x)  16           -4

Your f(-1), f(0), and f(1) are all positive.
Your f(2) is negative.
Since the function is continuous in the interval x=1 to x=2 
The graph must cross the x-axis to get from + to -
Therefore there must be a zero between x=1 and x=2.

Cheers,
Stan H.