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Density estimate with bounds

Dear R users,

I would like to show the estimated density of a (0, 1) uniformly distributed random variable. The density curve, however, goes beyond 0 and 1 because of the kernel smoothing. 

Example:

x = runif(10000)
plot(density(x))

Is there a way to estimate the density curve strictly within (0, 1) and still use some sort of smoothing?

Any help would be greatly appreciated.

Best regards,

Justine Rochon