Original
Let {{MATH_7}} be continuous on {{MATH_8}}. If {{MATH_9}} is {{CMD_10}}any{{CMD_11}}
antiderivative of {{MATH_12}}, then
{{MATH_13}}
{{CMD_14}}
Call {{MATH_15}} the accumulation function given by
{{MATH_16}}
By the First Fundamental Theorem of Calculus, {{MATH_17}} is an antiderivative of {{MATH_18}}. We see that both:
{{ENV_19}}
Fix {{MATH_20}} as any antiderivative of {{MATH_21}}. Since {{MATH_22}} and {{MATH_23}} have the same derivative, they differ by a constant.
That is, there is a constant {{MATH_24}} such that for any {{MATH_25}} in the interval {{MATH_26}}, {{MATH_27}}.
Then:
{{ENV_28}}
{{COMMENT_29}}
{{COMMENT_30}}
{{COMMENT_31}}
{{COMMENT_32}}
{{COMMENT_33}}
{{COMMENT_34}}
{{COMMENT_35}}
{{COMMENT_36}}
{{COMMENT_37}}
{{COMMENT_38}}
{{COMMENT_39}}
{{COMMENT_40}}
{{COMMENT_41}}
{{COMMENT_42}}
{{COMMENT_43}}
{{COMMENT_44}}
{{COMMENT_45}}
{{CMD_46}}
{{CMD_47}}