Property 3: `int_a ^b f(x) dx = int_a ^c f(x)dx + int_c ^b f(x) dx`

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

STATEMENT-1 : int_(-2pi)^(5pi)cot^(-1)(tanx)dx=7(pi^(2))/(2) and STATEMENT-2 : int_(a)^(b)f(x)dx=int_(a)^(c )f(x)dx+int_(c )^(b)f(x)dx , a lt c lt b

prove that : int_(0)^(2a) f(x)dx = int_(0)^(a) f(x)dx + int_(0)^(a)f(2a-x)dx

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