Formal Integral Definition:
f(x) dx = lim (d -> 0)
(k=1..n) f(X(k)) (x(k) - x(k-1))
a = x0 < x1 < x2 < ... < xn = b
d = max (x1-x0, x2-x1, ... , xn - x(n-1)) x(k-1) <= X(k) <= x(k) k = 1, 2, ... , n F '(x) dx = F(b) - F(a) (Fundamental
Theorem for integrals of derivatives)
a f(x) dx = a f(x) dx (if
a is constant)
f(x) + g(x) dx = f(x) dx + g(x) dx
f(x) dx = f(x) dx | (a b)
f(x) dx + 
f(x) dx = 
f(x) dx
f(u) du/dx dx = f(u) du (integration
by substitution)
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