Original
Definition: a Function 
is called the initial function 
on this interval, if any 
of this period 
Examples
- For functions
on the interval 
initial is 
because 
- For functions
on the interval 
initial is 
because 
on the interval 
initial is 
because 
on the interval 
initial is 
because 
The main property of the integral
If the function is the initial function on this interval and 
is an arbitrary constant, the function 
is also the initial function 
in this case, any primitive of the function on this interval can be written in the form 
where is an arbitrary became
The geometric meaning
Any graphics primitive of this function can be obtained from each other by parallel transfer along the axis 
Indefinite integral
Definition:the Set of all primitives of a given function is called the indefinite integral and is denoted by 
i.e., 
where one of the primitive functions and some became
Rules of integration
where 
became
