By symmetry, ∫ − 1 1 f ( x ) d x = 2 ∫ 0 1 f ( x ) d x {\displaystyle \displaystyle \int _{-1}^{1}f(x)dx=2\int _{0}^{1}f(x)dx} when f ( x ) {\displaystyle f(x)} is an even function.
