Building a function by defining X and Y and then Integrating in R

Question

I need to construct a function with x values coming from the first column of this matrix below and y values coming from the second column from the same matrix, with the purpose

Answer 1

When I looked at you provide matrix (better use variable mat not matrix for it), I found that your x samples are evenly spaced, and y values are monotone and smooth against x. So a simple linear interpolation would be sufficiently good to model those data.

## read `?approx`
f <- approxfun(mat[, 1], mat[, 2])

Then you can do

integrate (f, lower = 0.08, upper = 0.15)
# -0.2343698 with absolute error < 1.3e-05