Evaluate the definite integration

\(\rm\displaystyle\int_0^4 \)(x + 1) dx

and choose the right answer:

Given:

f(x) = \(\rm\displaystyle∫_0^4 \)(x + 1) dx

Calculation:

⇒  \(\rm\displaystyle∫_0^4 \)(x + 1)dx = \(\rm\displaystyle∫_0^4 \)x dx  + \(\rm\displaystyle∫_0^4 \)1 dx

⇒  \(\left[\dfrac{x^2}{2}\right]^4_0 \) + \(\left[x\right]^4_0 \)

⇒ \(\left[\dfrac{4^2}{2} - \dfrac{0^2}{2}\right]^4_0 \) + 4 - 0

⇒ 8 + 4 = 12

∴ \(\rm\displaystyle\int_0^4 \)(x + 1) dx = 12