That is to say: the integral of f(x) on [0 1] is equal to the area of figure A enclosed by the image of f(x) and the straight line X = 0, Y = 0, and X = 1;

Random simulation shows that a sesame seed is randomly sprinkled into a square B surrounded by four straight lines: x=0, y=0, x= 1, y =1;

Probability of falling within a = n1/n = area of a/area of b;

Because the square area =1; So the integral value = the area of a = n1/n.