If f(x+T) = f(x) for all x (period T), then:

1. integral(0 to nT) f(x) dx = n * integral(0 to T) f(x) dx
2. integral(a to a+T) f(x) dx = integral(0 to T) f(x) dx (shift invariance)
3. integral(a to a+nT) f(x) dx = n * integral(0 to T) f(x) dx

Common periods: sin x, cos x have period 2pi. |sin x|, |cos x| have period pi. tan x has period pi. $sin^2$ x has period pi.

Example: integral(0 to 5pi) |sin x| dx. Period of |sin x| is pi. 5pi = 5 periods. integral(0 to pi) |sin x| dx = integral(0 to pi) sin x dx = 2. Total = 5 * 2 = 10.