Property 14: `int_(a+nT) ^(b+nT) f(x) dx = int_a ^b f(x) dx` where T is the period of the f(x) and n is integer

Property 11: int_0 ^(nT) f(x)= n int_0 ^T f(x) dx where T is the period of the function and n is integer

Property 12:int_(a)^(a+nT)f(x)dx=n int_(0)^(T)f(x)dx where T is period of f(x)

Property 13:int_(mT)^(nT)f(x)dx=(n-m)int_(0)^(T)f(x)dx where T is period of f(x) and m and n are integer

int_(a + c)^(b+c) f(x)dx=

int _(a) ^(b) f (x) dx = int _(a) ^(b) f (a + b - x) dx

Prove that int_(a)^(b) f(x) dx= int_(a)^(b) f(a+b-x) dx

Property 3:int_(a)^(b)f(x)dx=int_(a)^(c)f(x)dx+int_(c)^(b)f(x)dx

Statement 1: int_(0)^(10)(2^(x))/(2^([x]))dx=(10)/(ln2) (where [.] denotes the greatest integer function) because Statement 2: int_(0)^(nT)f(x)dx=n int_(0)^(T)f(x)dx if T is the fundamental period of f(x), n is rational number.

If int_(n)^(n+1)f(x)dx = n^(2) , where n is an integer, then int_(-2)^(4)f(x)dx=