Leibnitz’s rule for differentiating an integral

Let
$\displaystyle I(a) = \int_{a}^{b}f(x, \alpha)dx$
where f is supposed continuous and differentiable. Then Leibnitz’s rule states that if a and b are differentiable functions of α,
$\displaystyle \frac{dI}{d\alpha} = \int_{a}^{b}\frac{\partial f}{\partial \alpha}dx + f(b, \alpha)\frac{db}{d\alpha} - f(a, \alpha)\frac{da}{d\alpha}$

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