Dear student,

For finding area of any curve you must know the integration.
Because the integration gives the area under curve.

So, this is a upward parabola passing through origin or having vertex at origin.
Now we are told to calculate the area from x= -1 to x = 1.
So, it will be a definite integration.
So, integration ( from x = -1 to x = 1) of x^2 dx = x^3 /3 and limit will be from -1 to 1.

So, the answer will be :-

1/3 - (-1/3) = 2/3.

So, area enclosed by curve y = x^2, the x axis and the lines x= -1 and x = 1 is :-
2/3