Thanks to @Ethan for introducing me to a new way of depicting the AUC.

I have figured out what was wrong in my code and fixed it. I am adding this as an answer for the sake of completion.

The issue was in the following line,

plot Intgrl=0 FILE u 1:(Intgrl+f(x),f(x)) w table

The function should be supplied with actual values $1 and not just the variablex. It should be as,

plot Intgrl=0 FILE u 1:(Intgrl+f($1), f($1)) w table

Following is the generated plot.