Difficulty in implementing equations & performing Function Integration (Error First input argument must be a function handle.)

I have been trying to implement the following equations but am having a problem with their implementation especially the third equation, which involves integration and takes the output value from the second equation.

Function f(Zb) is the Gaussian probability density function with mean 0 and SD 1, and function F(Zb) is the equivalent cumulative normal probability function.

I am sharing my code kindly specify what exactly am I doing wrong.

[num1, text1, raw1] = xlsread('C:\Users\Hawkins\Desktop\Excel Data\Daily Mean Temperature (North Las Vegas_July_2010).xlsx');
[num2, text2, raw2] = xlsread('C:\Users\Hawkins\Desktop\Excel Data\Monthly Mean Temperature (North Las Vegas_2010).xlsx');
prompt = 'What is the Base Temperature Value? ';
Tb = input(prompt)
Td1 = num1(:,[2]);
Tm1 = num2(:,[2]);
Td = Td1';
Tm = Tm1';
Sd = std(Td);
Zb = (Tb - Tm)/Sd;
%function fZb = NPDF (Zb) %This function is called later in the code 
%e1 = 1/(sqrt(2*pi));
%e2 = -(Zb.^2)/2
%fZb = e1 * exp(e2)
%end

NPDF (Zb)
fun = NPDF (Zb)
xmin = -Inf 
xmax = Zb
q = integral(fun,xmin,xmax)

Answer 1

[Torsten]

Your integral equals

0.5*(1+erf(Zb/sqrt(2)))

No need to use "integral" in this simple case.

Best wishes

Torsten.

[Hawkins]

Thank you Torsten, but can you please elaborate how my integral equals to the equation which you have stated. Cause I still couldn`t figure it out

[Hawkins]

I have also verified your response from here, but can you still please elaborate. http://www.mathworks.com/help/matlab/ref/erf.html

[Torsten]

Read the paragraph

"Find cumulative distribution function of normal distribution"

under

http://de.mathworks.com/help/matlab/ref/erf.html

Best wishes

Torsten.

[Hawkins]

Thanks you, best regards.