Unit of value calculated by using integral

Question

I have a really simple question that is driving me crazy! I have a program which can log power and the result is a log file which contains two arrays, one with time values that show when a power value was logged and one with the corresponding power values. The unit of the x-values is seconds and the unit of the y-values is watt. Sample output: \begin{equation*} x = [0, 1, 5, 100] \\ y = [0, 0.2, 0.5, 1] \end{equation*} Now I would like to calculate the total amount of energy during these 100 seconds. As the x-values are different I can't just add the y-values together, but have to use a function like the composite trapezoidal rule. My simple question is this: what unit will the value from trapezoidal(x, y) have? My first thought was watt-during-100-seconds, but I also think that it can be watt times second.

Answer 1

I have concluded that the answer to the question is watt-seconds. Just like when calculating an integral of velocity over time gives you v*t = s, caluclating an integral of power over seconds gives watt times seconds.