Mistake 1: Forgetting to change limits when substituting. If u = sin x and limits are x = 0 to pi/2, then u goes from 0 to 1 — do NOT keep x-limits.

Mistake 2: Applying King's Rule as integral(a,b) f(x) = integral(a,b) f(b-x). The correct formula is f(a+b-x), not f(b-x) (unless a = 0).

Mistake 3: Treating integral(-a,a) of any symmetric-looking function as 0. Check: is f(-x) = -f(x)? Only then is the integral 0. For example, integral(-1,1) $x^2$ dx != 0 ($x^2$ is even, not odd).

Mistake 4: Wrong Wallis factor. For even n, the answer contains pi/2. For odd n, it does NOT. Mixing these up is very common.

Mistake 5: Using FTC across a discontinuity. integral(-1,1) 1/$x^2$ dx is NOT -2. The function 1/$x^2$ -> infinity at x = 0, so the integral diverges.