To find the points of intersection, set the equations equal: \(2x + 11 = 8 - 2x - x^2\).

Rearrange to form a quadratic equation: \(x^2 + 4x + 3 = 0\).

Factorize: \((x + 1)(x + 3) = 0\).

Thus, \(x = -1\) or \(x = -3\).

To find the area between the curves, integrate the difference between the curve and the line from \(x = -3\) to \(x = -1\):

\(\int_{-3}^{-1} (8 - 2x - x^2) \, dx - \int_{-3}^{-1} (2x + 11) \, dx\).

Integrate each part:

\(\int (8 - 2x - x^2) \, dx = 8x - x^2 - \frac{x^3}{3}\).

\(\int (2x + 11) \, dx = x^2 + 11x\).

Evaluate from \(x = -3\) to \(x = -1\):

\([8(-1) - (-1)^2 - \frac{(-1)^3}{3}] - [8(-3) - (-3)^2 - \frac{(-3)^3}{3}]\).

\([8(-1) - 1 + \frac{1}{3}] - [8(-3) - 9 + \frac{27}{3}]\).

Calculate the definite integrals and subtract: \(\frac{4}{3}\).