function integral = Hw6Num1f(a, b, N)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Returns the approximate integral of sin(x^2)
% from a to b with N steps, using the left hand rule.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

	% calculate the discretization step, assuming N is an integer
	dx = (b - a)/N;
	% create our result variable
	integral = 0;
	% loop over the elements in the sum
	for k=0:(N - 1)
		% calculate the location for our function evaluation
		x = a + dx*k;
		% add
		integral = integral + sin(x^2)*dx;
	end
return
