Integrate over time return corresponding y value for predefined volume

This graph describes the problem well.

Given:

• time series with x (time [s]) and y (here discharge [m³/s])
• V1 = a value in the same dimension / unit as the result of the integration, smaller than the integral. Here a small volume [m³]

Needed:

• The y[m³/s] value, which leads to V1 if integration (minus the y values smaller) is started there.

The V1 must be placed around the peak.

I'm rather new to MATLAB.

I think this must be an iterative process, where also a the fitting criteria (and the degree of exactness) must be set by the user.

All in all an intersting task. Till now I haven't found a way to start; besides the pure integration.