Definite Integral of Function plus Constant

Theorem
Let $$f$$ be a real function which is continuous on the closed interval $$\left[{a \,. \, . \, b}\right]$$.

Let $$c$$ be a constant.

Then $$\int_a^b \left({f \left({t}\right) + c}\right) dt = \int_a^b f \left({t}\right) dt + c \left({b - a}\right)$$.

Proof
Let $$P$$ be a subdivision of $$\left[{a \,. \, . \, b}\right]$$.