Find the antiderivatives.
1. f(x)= x sin (x^2)
2. f(x)= x sin x
let u = x^2
du = 2x dx
and your integrand becomes
1/2 sin(u) du
for the 2nd one, use integration by parts
u = x
du = dx
dv = sin x dx
v = -cos x
∫u dv = uv - ∫v du
∫ x sinx dx = -x cos x + ∫cos x dx