Probably, you want to find the area between the curve and the x-axis.
This is
Above the x-axis it's
This is zero when x=0 and when x=1. For negative x, this would be complex.
Beyond x=1, the curve travels to infinity.
Therefore, integrate from x=0 to x=1,
and double your result if you want to include the region below the x-axis.
You can start by simplifying the powers of x.