The reason why the interval in the first line of interval reproduction formula is from A to B, then to B and then to A:

Dx=d(a+b-t)=-dt, A and B are constant derivatives, which are directly 0. The negative sign cancels the upper and lower bounds of the previous integral, and the upper and lower bounds should be interchanged.

The subtlety of interval regeneration formula is that the integrand function can be modified without changing the integral region. When trigonometric functions are mixed with complex exponential logarithms or ordinary polynomials (such as x* è Sinks è), and the integral region contains π/2, π, etc., the interval reproduction formula is suitable.