explain the codes below(which are the answer to the question) and tell their role stepwise(like a report) regarding the question.

format long

clear all

f = @(x) sin (x);

integrator(f,[0 1],1e-6)

%Main function

function integrator(f,t,er)

h=0.01;

n=abs(t(2)-t(1))/h;

cnt = 0;

prev = 0;

func(prev,f,t,h,n,cnt)

function func(prev,f,t,h,n,cnt ) %sub function

tic

cnt = cnt + 1;

%Simpson integration rule

I=(f(t(2))+f(t(1)));

for j = 1:2:n-1

I=I+4*f(t(1)+j*h);

end

for k = 2:2:n-2

I=I+ 2*f(t(1)+k*h);

end

answerS = I*(h/3) ;

if(abs(prev - answerS)1)

fprintf('Integral is: %f ',answerS)

fprintf('Total number of iterations taken: %d ',cnt)

return

elseif(cnt>100)

fprintf('Recursion depth More than 100!!! ')

fprintf('Integral is: %f ',answerS)

return

else

time = toc;

if(time >= 5*60)

fprintf('Compplex function!!!! Execution time more than 5 minutes !!!!')

return

end

func(answerS,f,t,h/2,2*n,cnt) %Recurssion

end

end

return

end

General Integrator Develop a general purpose Matlab integrator that will integrate an arbitrary bounded function on an arbitrary interval. Your function should be called as follows: >>integrator('sin(x)', [01], 1e-6) where the third argument as an upper bound on the absolute error. The last argument should be optional (with le-6 being the default). The main challenge in this project is error control since you don't know the true answer So start the following by letting h=0.01 and using Simpson's rule. Then proceed to divide h by 2. When the answer states changing by less than 0.1*(requested error), consider that is the area of the answer. If that never starts happening, which means that the input function is too complex, display an error. Keep track of how long the previous step took and if the following step would take more than 5 minute prompt the user on whether to proceed. Save time by subdividing the segment into 2 halves and working with cach half separately. Make your function recursive (you will need to write a sub-function), but don't allow the recursion depth to exceed more than 100