Property 4: If `f(x)` is a continuous function on `[a,b]` then `int_a ^b f(x) dx = int_a ^b f(a+b-x) dx`

Property 5: If f(x) is a continuous function defined on [0;a] then int_(0)^(a)f(x)dx=int_(0)f(a-x)dx

Property 8: If f(x) is a continuous function defined on [-a;a] then int_(-a)^(a)f(x)dx=int_(0)^(a){f(x)+f(-x)}dx

Property 9: If f(x) is a continuous function defined on [-a;a] then int_(-a)^(a)f(x)dx=0 if f(x) is odd and 2int_(0)^(a)f(x)dx if f(x) is even

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

Property 6: If f(x) is a continuous function defined on [0;2a] then int_(0)^(2)a=int_(0)^(a)f(x)dx+int_(0)^(a)f(2a-x)dx

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

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

int_a^b[d/dx(f(x))]dx