Two differentiable functions $f(x)$ and $g(x)$ are such that $f''(x) > 0$ and $g''(x) < 0$ for all $x \in (a,b)$ and $\int_{a}^{b} f(x) dx = \int_{a}^{b} g(x) dx$. If $f(x) = g(x)$ for $x = \alpha, \beta \in (a,b)$ $(\alpha < \beta)$,then:

• A
  $\int_{\alpha}^{\beta} (g(x) - f(x)) dx = \int_{a}^{\alpha} (f(x) - g(x)) dx + \int_{\beta}^{b} (f(x) - g(x)) dx$
• B
  $\int_{\alpha}^{\beta} (g(x) - f(x)) dx = \int_{a}^{\alpha} (f(x) - g(x)) dx$
• C
  $\int_{\alpha}^{\beta} (g(x) - f(x)) dx = \int_{\beta}^{b} (f(x) - g(x)) dx$
• D
  $\int_{\alpha}^{\beta} (g(x) - f(x)) dx = \int_{\alpha}^{\beta} (f(x) - g(x)) dx$