Math 252 the fundamental theorem of calculus find the

Question

The Fundamental Theorem of Calculus

(1) Below is the part of the graph of a function f(t). Let F(x) = ₀∫^x f(t)dt

(a) Find F(4.5).

(b) Find F'(4.5).

(c) Find F"(4.5).

(d) Find the minimum and maximum values of F(x) on [0, 5].

(e) Suppose it is given that _-2∫²f(t)dt = 5. Find _-2∫^-1f(t)dt.

(2) Suppose that f is a continuous function and that f(3) = 3, f(6) = 5.

Let G(x) = ₁∫^{x^2}f(t)dt. Find G'(3).

(3) Suppose that f is a continuous function and that f(1) = 1, f(3) = -4.

Let H(x) = _x∫¹⁰f(t)dt. Find H'(2).

(4) Suppose that f is a continuous function and that f(2) = 5, f(3) = 2,

Let K(x) = _√x∫^xf(t) dt. Find K'(4).

(5) Suppose F'(x) = f(x) and we are given F(1) = 10, F(2) = 5, F(10) = 1.

Find ₁∫⁵f(x)dx.

(6) Find x such that _-1∫^x (1/1+t²)dt = (7π/12).

I need all the steps and finish.