You can plot this function in Mathematica using:

```
Plot[Piecewise[{{0.075 x + 2, 3 <= x && x <= 5}},
0], {x, 0, 5}]
```

And then verify area using definite integral (from 0 to infinity):

```
Integrate[Piecewise[{{0.075 x + 0.2, 3 <= x && x
<= 5}}, 0], {x, 0, Infinity}]
```

(which results in 1).

You can of course calculate it by hand.

Integral represents area under the curve. When `x`

is not in
range `[3,5]`

then area is always zero.

So your problem can be reduced to calculating integral from ```
0.075
x + 0.2
```

, between `3`

and `5`

.

Integral from `(0.075 x + 0.2)dx`

equals to ```
0.2 x +
0.0375 x^2 + C
```

. When calculated in range, equals to ```
1.9375 -
0.9375 = 1
```

.