plot integral of cdf

prob_mat_1 = cbind(sort(rnorm(88)), rep(1/88, 88), cumsum(rep(1/88, 88)))
prob_mat_2 = cbind(sort(rnorm(88)), rep(1/88, 88), cumsum(rep(1/88, 88)))
cdf_int_f = function(prob_mat){
  h = tail(prob_mat[,1], nrow(prob_mat)-1) - head(prob_mat[,1], nrow(prob_mat)-1)
  u_plus_l = tail(prob_mat[,3], nrow(prob_mat)-1) + head(prob_mat[,3], nrow(prob_mat)-1)
  cumsum(h*u_plus_l/2)
}
plot(prob_mat[2:nrow(prob_mat_1),1], cdf_int_f(prob_mat_1), type = "l")
lines(prob_mat[2:nrow(prob_mat_2),1], cdf_int_f(prob_mat_2), col = 2)