If the following function is a probability density function of a random variable $X$, $f(x) = kx^2(1 - x)$ for $0 < x < 1$ and $f(x) = 0$ otherwise, then the value of $k$ is:
- A$-12$
- B$\frac{1}{12}$
- C$\frac{1}{6}$
- D$12$
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