Find the area of the figure bounded by the given lines y = x ^ 2-4, y = 0, x = 0, x = 1

The parabola intersects the Ox axis at the points x = -2 and x = 2, its vertex has coordinates (0; -4). Therefore, you need to find the area of the parabola in the range x from 0 to 1 under the Ox axis. This area will be equal to:

s = -integral (from 0 to 1) (x² – 4) dx = -x³ / 3 + 4 * x (from 0 to 1) = -1 / 3 + 4 – 0 = 11/3 units².

Answer: the required area of the bounded figure is 11/3 units ².