Use integration by parts

Let, x = sin t

⇒ dx = cos t dt

At x = 0, t = 0

At x = 1, t = π/2

Use integration by parts

Let, …(1)

Use King theorem of definite integral

…(2)

Adding eq.(1) and eq.(2)

Let, 2t = z

⇒ 2 dt = dz

At t = 0, z = 0

At t = π/2, z = π