Consider the function g defined on the interval [0,4] whose derivative is
g′(x)=e2x−3.
It is known that g(0)=4.
(a) Find an explicit formula for g(x) on 0≤x≤4.
(b) Evaluate g(2).
(c) Compute ∫02g′(x)dx and compare the result with g(2)−g(0). State the theorem that supports your comparison and explain its significance in this context.