#### 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