How to use function parity to solve definite integral?  

How to use function parity to solve definite integral?  

First judge that the original function is an odd function f (x) = - f (- x)
The upper and lower limits of the integral are symmetric about the origin, so the integral is 0
Indefinite integral can be obtained by the area of function
The area formed by the symmetric part of an odd function about the origin on the X axis is 0
The indefinite integral of odd function with upper and lower limit symmetric about 0 is also 0

What is the relationship between the symmetry, periodicity and parity of functions?

(1) The monotonicity of odd function in symmetric interval is the same, but the monotonicity of even function in symmetric interval is opposite. (2) parity is a special symmetry, that is, parity property deduces symmetry, but symmetry cannot deduce parity