Determine whether each of the following statements is true or false. If the statement is true, provide an appropriate justification. If the statement is false, provide a counterexample.(a) If $f ( x ) \neq 0 \text { on } [ a , b ] \text { then } \int _ { a } ^ { b } f ( x ) d x \neq 0$ (b) If $f$ is continuous on an interval containing a,b, and c, then $\int _ { a } ^ { b } f ( x ) d x = \int _ { a } ^ { c } f ( x ) d x - \int _ { b } ^ { c } f ( x ) d x$ (c) If $\int _ { a } ^ { b } f ( x ) d x \geq 0 , \text { then } f ( x ) \geq 0 \text { on } [ a , b ]$

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The Answer of Determine whether each of the following statements is true or false. If the statement is true, provide an appropriate justification. If the statement is false, provide a counterexample.(a) If $f ( x ) \neq 0 \text { on } [ a , b ] \text { then } \int _ { a } ^ { b } f ( x ) d x \neq 0$ (b) If $f$ is continuous on an interval containing a,b, and c, then $\int _ { a } ^ { b } f ( x ) d x = \int _ { a } ^ { c } f ( x ) d x - \int _ { b } ^ { c } f ( x ) d x$ (c) If $\int _ { a } ^ { b } f ( x ) d x \geq 0 , \text { then } f ( x ) \geq 0 \text { on } [ a , b ]$

Determine Whether Each of the Following Statements Is True or False