When you load in the image the data type is uint8 - unsigned 8 bit integers. So you can't get values between 0 and 1 unless you change the data type:
I = imread('101_img_.png');
I = im2double(I);
Your following calculations should go as expected now:
[R,C,~]=size(I);
Red = I(:,:,1);
Green = I(:,:,2);
Blue = I(:,:,3);
red_norm = zeros(size(Red));
red_norm = (Red - min(Red(:)))./(max(Red(:))-min(Red(:)));
green_norm = zeros(size(Green));
green_norm = (Green - min(Green(:)))./(max(Green(:))-min(Green(:)));
red_norm_sum = sum(red_norm(:));
