I did not understand one thing if this equation y=x^3-x represents this curve then for x=1 how the value of y is 0.
To say the truth, I don’t quite understand your question.
If f(x) = x^3-x, then f(1) = 1^3 – 1 = 0. But surely you couldn't mean this was not clear
Or do you mean that from the graph, it is not clear that y=0 exactly for x=1 and not for some other x?
If so, let’s look at the graph. There are no numbers under the axis, so technically you are right and we cannot say – solely from the graph – what are the values of the roots (or the points of x-axis intercepts). However, we can say that there are three distinct roots: one is 0 and the other two are symmetrical relative to the y-axis. This condition, along with the fact that y>0 for large values of x, allows us to choose the only suitable answer. And, from the answer we have chosen (but not from the graph itself!), we can see that the roots are indeed 0, -1, 1.
However, if among the answer choices were something like y=x(x-2)(x+2) as well as y=x(x-1)(x+1), I think we could not have chosen between these two options – because the graph (which is not scaled) does not give us enough information to do so.
If I am mistaken about the intended meaning of your question – please, let me know; I'll try to explain better.