The graph of y = f^(-1)(x) is the reflection of y = f(x) about the line y = x. This means the area between y = f(x) and the y-axis from y = c to y = d equals the area between y = f^(-1)(x) and the x-axis from x = c to x = d. A useful identity: if f(a) = c and f(b) = d, then the integral from a to b of f(x) dx + integral from c to d of f^(-1)(y) dy = bd - ac. This is the "rectangle complement" identity and can save significant computation. For instance, to find the integral from 0 to 1 of sin^(-1)(x) dx, use the identity with f(x) = sin(x): integral from 0 to 1 of sin^(-1)(x) dx = 1 * pi/2 - integral from 0 to pi/2 of sin(y) dy = pi/2 - 1.