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

Prove that \int_{a}^b f(x) dx = \int_{a}^c f(x) dx + \int_{c}^b f(x) dx , a < c < b

Prove that 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

int_(a)^(b)f(x)dx=int_(b)^(a)f(x)dx .

Which of the following is incorrect? int_(a+ c)^(b+c)f(x)dx=int_a^bf(x+c)dx int_(ac)^(b c)f(x)dx=cint_a^bf(c x)dx int_(-a)^af(x)dx=1/2int_(-a)^a(f(x)+f(-x)dx None of these

Which of the following is incorrect? int_(a+ c)^(b+c)f(x)dx=int_a^bf(x+c)dx int_(ac)^(b c)f(x)dx=cint_a^bf(c x)dx int_(-a)^af(x)dx=1/2int_(-a)^a(f(x)+f(-x)dx None of these

If | int_a ^b f(x) dx| = int_a ^b |f(x)| dx, a lt b , then f(x) = 0 has