To do this, we need to show that the integral of $f$ over its domain (0 to 1) is equal to 1. So, we calculate the integral:
$$\int_{0}^{1} f(x) dx = \int_{0}^{1} 30x^{2}(1-x)^{2} dx = \frac{1}{3} + \frac{1}{5} - \frac{1}{2} = 1$$
So, the given function is a
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