Because the integrand contains absolute value sign, it is necessary to discuss the sign of t 2-x 2 in order to dilute the absolute value sign.

Because the domain of T is [0, 1], the domain of X is (0, 1).

So, when t

|t^2-x^2|=x^2-t^2

When x =x^2

|t^2-x^2|=t^2-x^2

Secondly, using the additivity of definite integral in finite interval. The definite integral value in the interval [0, 1] = the sum of the definite integral values in the interval [0, x] and [x, 1].

The integral of f (x) = (x 2-t 2) dt on [0, x]+the integral of f (t 2-x 2) dt on [x, 1].