Let

Let sin x- cos x=t

⇒ (cos x + sin x)dx=dt.

When x=0, t=-1 and , t=1.

Also, t²=(sin x – cos x)²

=sin²x+cos²x-2sinxcosx

=1-2sinxcosx

or

Hence

Let t=sin y

⇒ dt=cos y dy.

Also, when t=-1,

and when t=1, .