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`

Explanation

Given: `int_(-a) ^a f(x) dx = int_0 ^a {f(x) + f(-x)} dx`

As, `int_a ^b f(x) dx=int_a ^c f(x) dx+ int_c ^b f(x) dx `

`int_(-a) ^a f(x) dx=int_(-a) ^0 f(x) dx+ int_0 ^a f(x) dx `

`int_(-a) ^a f(x) dx=int_0 ^a f(x) dx+I_1`

`I_1=int_(-a) ^0 f(x) dx`

Let `x=-t implies dx=-dt`
And limits changes as `x=-a implies t=a` and `x=0 implies t=0`

`I_1=int_a ^0 f(-t) (-dt )`

...