If a function f(x) has an anti-derivative F(x), the area under the curve from a to b is equal to F(b)-F(a).

This is integration defined.

I've been jabbed

Given that dy/dx = 12x^2 + 4x - 5, find an expression for y.

y = 12((x^3)/3) + 4((x^2)/2) - 5((x^1)/1)

It would seem that
y=4x^3 + 2x^2 - 5x

but that is not quite the complete answer

Whenever you differentiate a constant you get zero,
e.g. y = 7 dy/dx = 0
and so the expression for y above could have any constant on the end and still satisfy dy/dx = 12x^2 + 4x - 5
The answer to this example is therefore
y= 4x^3 + 2x^2 - 5x + c, where c is a constant.

(Fruit poisoning) <------not good

Integration sucked when Elvis was around