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How can I solve the following attached calc problem?

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Sample problem:
\[\int_a^b (f(t)+g(t)) dt=\int_a^b f(t)dt+\int_a^b g(t)dt\]

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Other answers:

\[\sqrt[3]{t} = t ^{1/3}\]
\[\int\limits_{-1}^{1}t ^{1/3}-4\]
Do you know what to do from there?
Do you have a calculus textbook?
This is one of the first things you learn when integrating variables.
Yes but problems like these aren't provided as examples. These are basically challenges.
Add one to the exponent and divide the term by that sum.
\[\int\limits_{}^{}t ^{1/3} = {3 \over 4}t ^{4/3}\]
\[\int\limits_{?}^{?}-4 dt = -4t\]
3/4t^4/3 - 4t
then: (3/4-4)-(3/4+4). Right?
\[{3 \over 4}t ^{4/3}-4t\]
Close. (-1)^(4/3) = -1
{(3/4) - 4} - {(-3/4) + 4}
Answer: -8
What about this:
No. Not -8
But that's what I plugged in and it's right.
You had the equation worked out wrong. I said "Close".
I mean, expression. You had the expression written out wrong based on the -1.

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