This is the use of definite integration.
$\int_{a}^{b}f(x)dx=\int_{a}^{b}f(a+b-x)dx$
and some thing we should know
$cos(0)=1,cos(\pi)=-1,cos(2\pi)=1,.....$
in general $cos(n\pi)=(-1)^{n}$ where $n=0,1,2,...$
$sin(0)=0,sin(\pi)=0,sin(2\pi)=0,....$
in general $sin(n\pi)=0$ where $n=0,1,2,...$
and $sin(\pi-x)=sinx,sin(2\pi-x)=-sinx,sin(3\pi-x)=sinx$
in general $sin(n\pi-x)=(-1)^{n+1}sinx$ where $n=0,1,2,,...$
and $cos(\pi-x)=-cosx,cos(2\pi-x)=cosx,cos(3\pi-x)=-cosx,$
in general $cos(n\pi-x)=(-1)^{n}cosx$ where $n=0,1,2,...$
$f(x)=sinx$
$f(x)=cosx$