Hi I have a panel dataset with t=35 and n=300. For a project I need to run a regression of the following form.

Array

Where Y is the dependent variable (denoting total production) and T is the independent variable (denoting temperature deviations during a period z within a longer time period t (i.e. 𝑧∈𝑡)) for a production unit u within a larger unit i (i.e. 𝑢∈𝑖)
My problem is while I have run fixed effects regressions in the past, I have not dealt with an independent variable that is an integral.
Reading around a bit I find that integ can be used. However, I am not sure if it would help me to calculate the term above.
Any suggestions would be helpful