How integral of 0 is C???

Question

Toady I read that integral of 0 is C. because integral = antiderivative.

How can this be true, because we know that an integral is the area under a curve...and there is no area under the line x = 0, then how its area will be any Constant(after integrating the curve)

Answer 1

Fundamental theorem of calculus:

$$\int_a^bf(x)\ dx=F(b)-F(a)$$

For your case:

$$\int_a^b0\ dx=C-C=0$$

Answer 2

You're confusing definite and indefinite integrals.

A definite integral $\int_a^b \cdots dx$ can (under some common conditions) be interpreted as the area under a curve, but an indefinite integral $\int \cdots dx$ cannot -- it's not even a number but a function (well, a family of functions) defined simply by the requirement that its derivative must be the integrand.