How to normalize different curves drawn with geom = "step" when using stat_summary

Here is my code. The data set is artificially generated to simulate data similar to my actual problem.

Code:

library(ggplot2)
DataSet1 <- data.frame("Cat" = rep("A",10000), "Bin" = rep(c(-49:50),100), 
                       "Value" = c(seq(0,4.9, by=0.1),
                                   seq(4.9,0, by=-0.1)) * rep(rnorm(100,50,1),100))
DataSet2 <- data.frame("Cat" = rep("B",10000), "Bin" = rep(c(-49:50),100), 
                       "Value" = c(seq(0,4.9, by=0.1),
                                   seq(4.9,0, by=-0.1)) * rep(rnorm(100,75,1),100))
DataSet3 <- data.frame("Cat" = rep("C",10000), "Bin" = rep(c(-49:50),100), 
                       "Value" = c(seq(0,4.9, by=0.1),
                                   seq(4.9,0, by=-0.1)) * rep(rnorm(100,100,1),100))
DataSet <- rbind(DataSet1, DataSet2, DataSet3)

d <- ggplot(data = DataSet, aes(Bin, Value, color = Cat))
d + stat_summary(fun.y = sum, geom = 'step', size = 1)

My result:

What I want to do:

Normalize each of these plots, i.e., divide the sum at each bin width by the total Value for that curve.