find the area enclosed between the x-axis and the curve, if y=x^3 and the straight line y=x
It's not clear what you mean. Some of the question may be missing.
To find an area between the x-axis and a curve we need a domain. What is the domain?
PS: The curve and the line intercept at (-1,-1), (0,0), and (1,1). Is that involved somehow?