Answer:
[tex]\frac{5}{3}x^3+\frac{9}{2}x^2-7x+8\\[/tex]
Step-by-step explanation:
Integrate your function with respect to x to get the non-differentiated form.
[tex]\int(5x^2+9x-7)dx=\frac{5}{3}x^3+\frac{9}{2}x^2-7x+c\\[/tex]
Plug in your known value of x to get your value for your constant
[tex]f(0) = 8\\ \frac{5}{3}(0^3)+\frac{9}{2}(0^2)-7(0)+c = 8 \\c=8[/tex]
This gives you your function to be
[tex]\frac{5}{3}x^3+\frac{9}{2}x^2-7x+8\\[/tex]
