How to find the sum of values of a function at mid point of every subinterval?

I am trying to run this code but don't know how to write code for finding value of function F at mid point of subinterval say, if my interval is [ti, ti+1] for i=0,1,2, n. and need to find sum of functional value at every (ti +ti+1)/2. I need to do it for Rsum2 in this code.

clc; clear all; format long
%%%%%%%%%%%%%%%%%%%%%%%%%%
alpha=0.8;% fractional index 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
TN=1      % time 
N=10
T0=0
tau=TN/N  
T=[T0:tau:TN]
X0=0
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
X(1)=X0
 
F =@(X,T)=X+T
 
for n=0:N-1
 
Rsum=0;
    for j=1:1:n+2
       Rsum=Rsum+2*F (j)
    end  
        
    Rsum2=0;
    for j=1:1:n+1
       Rsum2=Rsum2+4*F (j+1/2)
    end      
 
 X(n+2)=X(1) +(tau^alpha)*Rsum + (tau^alpha)*Rsum2
             
end
 

Answer 1

[Matt J]

If your function is vectorized, like in the following example, it is quite simple:

fun=@(tm) tm.^2+ sqrt(tm); %A vectorized function

n=8;
t=sort(rand(1,n)) %interval end points t(i)

t = 1×8

0.0157 0.1988 0.2703 0.3719 0.5549 0.6696 0.7340 0.7594

tmid = t(1:end-1)/2 +t(2:end)/2 %interval mid-points

tmid = 1×7

0.1073 0.2345 0.3211 0.4634 0.6122 0.7018 0.7467

result =  sum(fun(tmid))

result = 6.3528

[Mubashara Wali]

Matt J. Thanx for answering. I will surely try.

[Matt J]

You're welcome, but if it works, please Accept-click the answer.

[Mubashara Wali]

Matt J Actually its working when F is a function of T only, but having a problem when F is a function of two independent variables as I mentioned in my code that F =@(X,T)=X+T. I would really appreciate if you can help me in this regard.