Simple integration (area under the curve) - help I'm currently doing a simple integration question: 

Here is my working/solution so far:

I have calculated this several times and only be seem to be getting a negative number as the final result. I know this is wrong as it is an area that needs to be calculated and therefore cannot be a negative number.
Any help on this is very much appreciated. Thank you!

It seems your work is in an image which is appearing weirdly on my screen. I'll just outline my work. 
$ \displaystyle\int \left( 5 + \dfrac{5}{4\sqrt{x}} - x^4 \right) \, \mathrm{d}x = \displaystyle\int 5 \, \mathrm{d}x + \displaystyle\int 4 \cdot x^{\frac{1}{2}} \, \mathrm{d}x - \displaystyle\int x^4 \, \mathrm{d}x $ 
$ = 5x + \dfrac {8}{3} x^{\frac{3}{2}} - \dfrac {x^5}{5} + \mathcal{C} $
Now, apply the limits of integration. At $ x = 3 $, the function value is $ \approx -19.7 $. At $ x = 2 $, the function value is $ \approx 11.1 $. The answer is, thus: $$ \approx -19.7 - 11.1 = \boxed {-30.8}. $$
