1. The maximum value of the function $y=\sin 2x + \sin x - \cos x$ on $\left[0, \frac{\pi}{2}\right]$ is
1. $\frac{5}{4}$.

Let $t=\sin x-\cos x=\sqrt{2} \sin \left(x-\frac{\pi}{4}\right) \in[-1,1]$, then
$$
y=\sin 2 x+\sin x-\cos x=-t^{2}+t+1=-\left(t-\frac{1}{2}\right)^{2}+\frac{5}{4} \leqslant \frac{5}{4} \text{, }
$$

where the equality holds when $t=\frac{1}{2}$.