The antiderivative of 
is, of course, itself. That makes evaluation of 
by the Fundamental Theorem trivial.
is, of course, itself. That makes evaluation of by the Fundamental Theorem trivial.format long, I = exp(1)-1
MATLAB has a built-in integral that estimates the value numerically without finding the antiderivative first. As you can see here, it's often just as accurate.
integral(@(x) exp(x),0,1)
The numerical approach is far more robust. For example, 
has no useful antiderivative. But numerically it's no more difficult.
has no useful antiderivative. But numerically it's no more difficult. integral(@(x) exp(sin(x)),0,1)
When you look at the graphs of these functions, what's remarkable is that one of these areas is the most basic calculus while the other is almost impenetrable analytically. From a numerical standpoint, they are practically the same problem.
x = linspace(0,1,201)';
subplot(2,1,1), fill([x;1;0],[exp(x);0;0],[1,0.9,0.9])
title('exp(x)') % ignore this line
ylabel('f(x)') % ignore this line
subplot(2,1,2), fill([x;1;0],[exp(sin(x));0;0],[1,0.9,0.9])
title('exp(sin(x))') % ignore this line
xlabel('x'), ylabel('f(x)') % ignore this line
