Code:

import sympy

x, y = sympy.symbols('x y')

# Define the curves
y1 = 1 - x**2
y2 = x**2 - 3

# Find intersection points
intersection_points = sympy.solve(y1 - y2, x)
x_min = min(intersection_points)
x_max = max(intersection_points)

# Set up the double integral for area: Integral from x_min to x_max of Integral from y2 to y1 of 1 dy dx
# Note: y1 (1-x^2) is the upper curve and y2 (x^2-3) is the lower curve in this interval
inner_integral = sympy.integrate(1, (y, y2, y1))
area = sympy.integrate(inner_integral, (x, x_min, x_max))

print(f"{intersection_points=}")
print(f"{x_min=}")
print(f"{x_max=}")
print(f"{inner_integral=}")
print(f"{area=}")

Output:

intersection_points=[-sqrt(2), sqrt(2)]
x_min=-sqrt(2)
x_max=sqrt(2)
inner_integral=4 - 2*x**2
area=16*sqrt(2)/3