The algorithm is as follows

• Choose the number of Monte Carlo samples $N$.
• Perform a loop over $N$ and for each step generate a random number $x_i$ in the interval $[0,1]$ through a call to a random number generator.
• Use this number to evaluate $f(x_i)$.
• Evaluate the contributions to the mean value and the standard deviation for each loop.
• After $N$ samples calculate the final mean value and the standard deviation.