Why the Integral and the Area Disagree

Porque é que o Integral e a Área Não Coincidem

For the curve $y = x^{2} - 4$, evaluate $\int_{0}^{3} \left(x^{2} - 4\right) \, dx$, find the total area enclosed between the curve and the $x$-axis for $0 \le x \le 3$, and explain why the two answers differ.