How do I calculate area?

Question

How do I calculate the area of this:

$D=\{ (x,y)\mid 0 \le x \le 1, x^2 \le y \le x^2+2 \}$

${A}=\iint_D \, \textrm{d}A.$

Don't know what is the right answer but I have get that the area is 6. Is that right answer?

Answer 1

$A = \int_0^1 dx \int_{x^2}^{x^2+2} 1 dy = \int_0^1 dx \cdot (x^2 + 2 - x^2) = \int_0^1 dx \cdot 2 = 2$