Final answer:
The Second Fundamental Theorem of Calculus states that the derivative of a function that is the integral of another function is equal to the original function. To find F(x), differentiate the given function and integrate it back to obtain F(x) = (1/5) * t^5 + 5t + C, where C is the constant of integration.
Step-by-step explanation:
The Second Fundamental Theorem of Calculus states that if the function F(x) is the integral of f(t) with respect to t from a constant a to x, then the derivative of F(x) with respect to x is equal to f(x).
In this case, F(x) = ∫(t⁴+5) dt from -1 to x. To find F(x), we first need to find f(x) by differentiating t⁴+5 with respect to t. The derivative of t⁴+5 is 4t³.
Therefore, F(x) = ∫(t⁴+5) dt = (1/5) * t⁵ + 5t + C, where C is the constant of integration.