# If int_a^b f(x) dx = a+2b, then what is int_a^b (f(x) + 5) dx equal to

If $$\int_{a}^{b} f(x)dx = a+2b$$ then $$\int_{a}^{b} (f(x)+5)dx = ?$$

Here's what I did:
$$\int_{a}^{b} (f(x)+5)dx = \int_{a}^{b}f(x)dx+\int_{a}^{b} 5 dx$$
$$\int_{a}^{b}f(x)dx+\int_{a}^{b} 5 dx = a+2b + 5b - 5a$$
$$\int_{a}^{b} (f(x)+5)dx = 7b-4a$$

Did I do this correctly? I know the answer is correct but I want to know if my thought process was correct or not. Thanks