To determine

To find:

Derivative of thegiven function

Answer

F'x=x21+x3

Explanation

1) Concept:

First, the Fundamental Theorem of Calculus

 If f is continuous on a, b, then the function g defined by

gx=∫axf(t)dt

is continuous on a, b and differentiable on (a, b), and g'x=f(x)

2) Given:

Fx=∫0xt21+t3 dt 

3) Calculation:

By using the first Fundamental Theorem of calculus

From the given function,

ft=t21+t3

Replace t by x,

fx=x21+x3

F'x=fx=x21+x3

Hence derivative of thefunction is x21+x3

Conclusion:

Therefore,

F'x=x21+x3