Arithmetic vs. integration

The contradiction in the article "intelligence test" (which I could not explain), does not know what number to count the number of prime numbers with a zero or a number (P_n). But, leaving this issue to others, I
the initial point of reference taking the number 0. And calculate the number of primes in the interval

by the formula

    Arithmetic vs. integration

 Go to the interval

 makes it possible to calculate the number of composite numbers. Subtracted 4.5 from the formula throw. More specifically, the error increases by calculating the number of 4.5, which does not affect the subsequent arguments.

If the formula

is a formula for the state. the formula

This is the formula process. Calculate the number of composite numbers in the interval

by the formula

makes it possible to accept the formula

for the derivative. And to state the problem: Let

is the derivative of the function F (x). The function F (x) the primitive of the function

Evaluate the integral

 In the integral calculus of great opportunities, I suggest you use them. I will go its own way. We then compare the results. And evaluate which one is more accurate.
Sergey Sitnikov