Prove that if (left(alpha_{s}, s geq 0 ight)) is an increasing predictable process and (X) a positive

Prove that if \(\left(\alpha_{s}, s \geq 0\right)\) is an increasing predictable process and \(X\) a positive measurable process, then

\[\left(\int_{0}^{\cdot} X_{s} d \alpha_{s}\right)_{t}^{(p)}=\int_{0}^{t}{ }^{(p)} X_{s} d \alpha_{s}\]

In particular

\[\left(\int_{0}^{\cdot} X_{s} d s\right)_{t}^{(p)}=\int_{0}^{t}{ }^{(p)} X_{s} d s\]