function [ output_args ] = riemann_sum( a, b, n )
dx = (b-a)/n;

r_sum = 0;
for i=1:n %this begins our for-loop to perform the right-summation for our
    %chosen function
    r_sum = r_sum + (exp(-(a + i*dx)^2))*dx; %you'll modify this function for
    %whatever you'd like to sum; here, we're using f(x) = e^x
end

l_sum = 0;
for i=0:(n-1) %this begins our for-loop to perform the left-sum for our
    %chosen function
    l_sum = l_sum + (exp(-(a + i*dx)^2))*dx; %you'll modify this function for
    %whatever you'd like to sum; here, we're using f(x) = e^x
end
m_sum = 0;
for i=0:(n-1) %this begins our for-loop to perform the left-sum for our
    %chosen function
    m_sum = m_sum + (exp(-(a + (i-0.5)*dx)^2))*dx; %you'll modify this function for
    %whatever you'd like to sum; here, we're using f(x) = e^x

end
t_sum = 0;
for i=0:(n-1) %this begins our for-loop to perform the left-sum for our
    %chosen function
    t_sum = t_sum + (exp(-(a + i*dx)^2)+exp(-(a+(i+1)*dx))^2)*dx/2; %you'll modify this function for
    %whatever you'd like to sum; here, we're using f(x) = e^x
end
r_sum
l_sum
m_sum
t_sum

%the above two lines display the sums we obtained. r_sum is the right sum,
%and l_sum is the left sum.

% PROJECT
%
% Part 1:
%
% Attempt to compute the following i) analytically and ii) numerically:
% exp(x^2) from 0 to 5
% sin(x^2) from 0 to pi/2
%
% Part 2:
%
% Modify the code to also yield a middle sum (ie, the height of each
% rectangle comes from the function value at the midpoint of each interval,
% rather than from the left-most or right-most point of each interval.)
%
% Bonus:
%
% Modify the code to also yield a trapezoidal sum (ie, computing the area
% under the curve using trapezoids instead of rectangles.)
%

end