Prove (without using the following Proposition!) that the process (left(int_{0}^{t} N_{s-} d M_{s}, t geq 0 ight)) is a martingale, and that the process (int_{0}^{t}

Prove (without using the following Proposition!) that the process \(\left(\int_{0}^{t} N_{s-} d M_{s}, t \geq 0\right)\) is a martingale, and that the process \(\int_{0}^{t} N_{s} d M_{s}\) is not a martingale.