Definite integral

Evaluate d/dα ∫(α->α²) sin(αx) / x dx，where α>0

I have two Methods

Method1：
dL/dα ∫(α->α²) sin(αx) / x dx
= sin(α³) / α² * (2α) - sin(α²) / α * 1
= 2sin(α³) / α - sin(α²) / α
= (1/α)[2sin(α³) - sin(α²)]

Method2：
L(α) = ∫(α，α²) sin(αx) / x dx
Let t = αx，dt = αdx => dx = (1/α)dt
When x = α，t = α²；whenx = α²，t =α³
L(α) = ∫(α²，α³) sin(t) / (t/α) * (1/α)dt
= ∫(α²，α³) sin(t) / t dt
= dL/dα = sin(α³)/α³ * (3α²) - sin(α²)/α² * (2α)
= 3sin(α³) / α - 2sin(α²) / α
= (1/α)[3sin(α³) - 2sin(α²)]

The answers obtained from two ways are different，
I want to ask which Method is correct?