B-spline curve is not satisfying partition of Unity property at the beginning and end

Question

At the beginning and end, the curve goes to zero

The following is the matlab code

clear,clc;
%%
p = 3; % degree
n = 10; % no.of control points
% control points
x = [1 0.5 5 3  11 8 12 11 15 17];
y = [4 6   4 12 14 4 3  9  10 8];

m = p + n + 1; % no.of knot vector
% specifying t(1:p) = 0, t(m-p:m) = 1
t = zeros(1,m);
t(1:p-1) = 0;
t(end:-1:end-p) = 1;
t(p : end-p+1) = linspace(0,1,size(p:m-p+1,2));

%%
cx = 0; cy = 0;
t_req = 0 : 0.01: 1;

px = zeros(size(t_req));
py = zeros(size(t_req));
pb = zeros(size(t_req));
params.m = m; params.p = p;
params.n = n;

b = zeros(size(t_req,2),size(x,2));

for ct = 1 : size(t_req,2)
    cx = 0; cy = 0; b = 0;

    for idx = 1 : size(x,2)

        basis_fun = N(idx,p,t,t_req(ct),params);

        b = b + basis_fun;
        cx = cx + x(idx)*basis_fun;
        cy = cy + y(idx)*basis_fun;
    end

    px(ct) = cx;
    py(ct) = cy;
    pb(ct) = b;
end


%% plotting
figure;
plot(px,py,'b','linewidth',1.3),grid,hold on;
plot(x,y,'r*-.','MarkerSize',7);


%% function to calculate basis_functions
function basis_fun = N(idx,p,t,t_req,params)

if ( p == 0 )
    if (t(idx) <= t_req && t(idx+1) > t_req)
        basis_fun = 1;
        return;
    else
        basis_fun = 0;
        return;
    end
else
    basis_fun = (t_req - t(idx))/(t(idx+p)-t(idx)) * N(idx,p-1,t,t_req,params) + ...
        (t(idx+p+1)-t_req)/(t(idx+p+1)-t(idx+1)) * N(idx+1,p-1,t,t_req,params);

    if (isnan(basis_fun) || isinf(basis_fun))
        basis_fun = 0;
    end

end
end