The Art of Integration

Finding an integral is basically just playing detective with numbers. If differentiation

is smashing a vase to see how it breaks, integration is gluing it back together to see what it looked

like. You are taking the rate of change and working backward to find the original

function. But here is the catch. You never get just one answer; you

get an infinite family of them. That is why you always have to add that plus C at the

end. It is not just a rule teachers annoy you with. It is the only time

in life where being vague is actually the correct answer.