Say I have a set of data points ($y$) measured at different times (hence a time series) which I know the uncertainties of the individual data points (in standard error). I connect them to form a line graph and find the area under curve (between time $0$ and the last time point) by integration. What would be the resultant standard error? I did the integration using auc in $R$ so I did not fit a equation to the line graph. From what I read so far, you need to fit an equation first to find such uncertainty, is there other way round? hopefully this is not a stupid question.


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