Area between curves

The area bounded by the curves $y = f (x)$ , $y = g (x)$ and the lines $x = 𝒶$ and $x = 𝒷$ , where $f (x)$ and $g (x)$ are continuous functions such that $\forall x \in [𝒶, 𝒷], f (x) \geq g (x)$ is

𝒜 = \int_{𝒶}^{𝒷} f (x) - g (x) d x .

The area bounded by the curves $y = f (x)$ , $y = g (x)$ and the lines $x = 𝒶$ and $x = 𝒷$ , where $f (x)$ and $g (x)$ are continuous functions is

𝒜 = \int_{𝒶}^{𝒷} | f (x) - g (x) | d x .

Find the area of the region bounded

above by $f (x) = 2 ℯ^{- x} + x$ ,
below by $g (x) = \frac{ℯ^{x}}{2}$ ,
on the left by $x = 0$ and
on the right by $x = 1$ .

Find the area between $f (x) = x + 4$ , $g (x) = 3 - \frac{x}{2}$ on $[1, 4]$ .

Find the area between $f (x) = 9 - \frac{x^{2}}{4}$ and $g (x) = 6 - x$ .

Find the area bounded by $f (x) = x^{2}$ , $g (x) = 2 - x$ and $x = 0$ . Express the area as a single integral in $y$ .