An antiderivative of a function is also known as integral of function. We are being ask to integrate the following function.
[tex]\int f(x)dx=\int 10x+3dx[/tex]
This function is relatively easy to integrate because its just a sum of terms with various exponents.
[tex]\int 10x+3dx=5x^2+3x+C[/tex]
To check, you can perform derivative on the function you got from antideriving. If it equals to the original function, then antiderivation procedure was done correctly.
[tex]\frac{d}{dx}5x^2+3x+C=10x+3=f(x)[/tex].
Et voilà.
Hope this helps.
