What is the average value for the top quarter of a sine wave?

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Say we have a sine wave with the peak value of 1. What is the average value of the top quarter of this sine wave? If you want some context it is for a diode question where the top quarter of a voltage is positive so im looking for the average voltage value of this part of the sine wave.

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Do you mean $$I=\frac{1}{b-a}\int_a^b\sin(x)\mathrm{d}x,$$ where $a$ is the value $x_1$ that results in $\sin(x_1)=\frac{3}{4}$ and $b$ is similarly $x_2$ such that $\sin(x_2)=1$?

Can you calculate the rest? If not, let me know.

I get

$I\approx 0.9152\dots$