DEFINITE INTEGRAL | PROPERTIES OF DEFINITE INTEGRALS | Property 5: If `f(x)` is a continuous function defined on `[0,a]` then `int_0 ^a f(x) dx = int_0^a f(a-x) dx`, Examples: `int_0 ^(pi/2) sinx / (sinx + cosx) dx`, Property 6: If f(x) is a continuous function defined on `[0, 2a]` then ` int_0 ^(2a)f(x)dx = int_0 ^a f(x) dx + int_0 ^a f(2a - x) dx`, Examples: `int_0 ^(2pi) 1 / ( 1 + e^sinx) dx`, Property 7: Let f(x) be a continuous function of x defined on `[0, a]` such that `f(a-x) = f(x)` then `int_0 ^a x f(x) dx = a/2 int_0 ^a f(x) dx`, Examples: `int_0 ^(pi/2) x / (sinx + cosx) 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`, Examples: `int_(-pi/2) ^(pi/2) 1 / (1 + e^sinx) dx`