Definite Integral Properties

Linearity:

∫[af + bg]dx = a∫f dx + b∫g dx

Additivity:

∫ from a to c = ∫ from a to b + ∫ from b to c

Reversal:

∫ from a to b = -∫ from b to a

Zero width:

∫ from a to a = 0

Comparison:

If f(x) ≥ 0 on [a,b], then ∫ from a to b f(x)dx ≥ 0

If f(x) ≥ g(x) on [a,b], then ∫f dx ≥ ∫g dx

Even function (symmetric about y-axis):

∫ from -a to a f(x)dx = 2∫ from 0 to a f(x)dx

Odd function:

∫ from -a to a f(x)dx = 0

AP exam: Uses these properties in problems where you can't evaluate the integral directly but can use given information to find the answer.

Reference:

Wikipedia: Integral

https://en.wikipedia.org/wiki/Integral