Let ` f ( x) = int _ 0 ^ x g (t) dt ` , where g is a non - zero even function . If ` f(x + 5 ) = g (x) ` , then ` int _ 0 ^ x f (t ) dt ` equals :

Options

A. (a) ` 5 int _ ( x + 5 ) ^ 5 g (t) dt `
B. (b)` 2 int _ 5 ^ ( x + 5) g (t) dt `
C. (c)` int _ 5^ ( x + 5 ) g (t ) dt `
D. (d)` int _ ( x + 5 )^( 5) g (t ) dt `

Explanation

To solve the problem step by step, we start with the given information:

Let \( f(x) = \int_0^x g(t) \, dt \), where \( g \) is a non-zero even function. We also know that \( f(x + 5) = g(x) \).

### Step 1: Analyze the function \( f(x) \)

Since \( g(t) \) is an even function, we have:

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