Answer: C

Small Hint:

Evaluate $\heartsuit(1),\heartsuit(2),\heartsuit(3)$ separately

Big Hint:

$\heartsuit(x)=\dfrac{x+x^2}{2}$

Solution:

We have $$\heartsuit(1) = \dfrac{1 + 1^2}{2} = 1,$$ $$\heartsuit(2) = \dfrac{2 + 2^2}{2} = 3,$$ and $$\heartsuit(3) = \dfrac{3 + 3^2}{2} = 6.$$

Then $$1 + 3 + 6 = 10.$$

Thus, C is the correct answer.